Photophysics of Aromatic Molecules 0471074209

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Photophysics of

Aromatic Molecules

WILEY MONOGRAPHS IN CHEMICAL PHYSICS Editor John B. Birks, Reader in Physics, University of Manchester

Photophysics of Aromatic Molecules: J. B. Birks, Department of Physics, University of Manchester Atomic & Molecular Radiation Physics: L. G. Christophorou, Oak Ridge National Laboratory, Tennessee

Photophysics of

Aromatic Molecules

John B. Birks Reader in Physics, University of Manchester

WILEY - INTERSCIENCE a division of John Wiley & Sons Ltd London New York Sydney Toronto

Copyright © 1970 John Wiley & Sons Ltd. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical photo-copying, recording or otherwise, without the prior written permission of the Copyright owner. Library of Congress catalog card number 70- 115934 ISBN 0 471 07420 9

Printed in Great Britain by Spottiswoode, Ballantyne & Co. Ltd. London and Colchester

This book is dedicated to past and present members of the Atomic and Molecular Physics Group at the University of Manchester.

v

Preface The scientific spectrum can be roughly divided into four broad bands or disciplines: mathematics, physics, chemistry and biology. In the regions of overlap of adjacent bands, the interdisciplinary areas of theoretical physics, chemical physics and biochemistry have developed. Chemical physics lies at the centre of the spectrum, in the area linking the physical sciences and the life sciences. Atomic and molecular physics developed rapidly between the wars with the application of quantum theory and high-resolution spectrometry to the study of atoms and simple molecules. The last two decades have seen similar advances in the study of the photophysics of aromatic molecules. There are six related subjects concerned with the interaction of radiation with molecular systems: photophysics, photochemistry and photobiology, which deal with optical non-ionizing radiation; and radiation physics, radiation chemistry and radiation biology, which deal with ionizing radiation. Photophysics is the keystone of the structure, since it is an integral constituent of each of the other five subjects. My own interest in the field arose initially from studies of the scintillation process in organic systems, and a realization that the primary radiation physical processes cannot be properly understood without a detailed knowledge of the resultant photophysical processes. Others have entered the field of photophysics, for similar or different reasons, from photochemistry, photobiology, radiation chemistry, theoretical chemistry, organic chemistry, biochemistry, molecular biology, spectroscopy, solid-state physics, theoretical physics, polymer science, nuclear instrumentation and laser technology, so that the subject has become a veritable interdisciplinary 'Place de la Concorde'. This book is written from the point of view of an experimental physicist, who appreciates both the uses and the limitations of quantum mechanics when applied to complex molecules. Theory has been kept to the essential mmlmum, since there are already many excellent books on quantum chemistry. Physics is the science of measurement, systematization and vii

viii

Preface

integration. The extensive compilations of data are designed to provide the raw material for interpretation and synthesis. In any dynamic science there are many areas of controversy. In discussing these I have tried to present the different viewpoints, including my own, as objectively as possible. In the words of Leonardo: 'Experiments never deceive. It is our judgment that sometimes deceives itself because it expects results which experiment refuses. We must consult experiment, varying the circumstances, until we have deduced reliable rules.' This book presents to the experimentalist the rules which are to be tested, and to the theorist the results which are to be explained. To avoid the complexities associated with heterocyclic molecules and with substituent groups which introduce n-7T electronic transitions, the discussion has been largely confined to the aromatic hydrocarbons and their simple derivatives. A systematic study of this group of molecules is a prerequisite to a proper understanding of the behaviour of more complex aromatic molecules. Writing a book about a subject which is advancing as rapidly as the present one is like trying to descend a rapidly mounting moving staircase. The final descent and the completion of the manuscript have only been achieved by relying on conferences, private discussions, preprints, correspondence and cursory glances at the journals for news of developments during the closing stages, and I am indebted to all who have thus supplied me with 'stop-press' material. Work which has come to my attention since the completion of the original manuscript has been summarized as a postscript in Chapter 12. My greatest debt is to my wife, who once again has ungrudgingly sacrificed a long period of personal companionship for the sake of science. Finally I wish to thank my secretary, Miss Clara Nicholls, for her meticulous and patient typing of the manuscript. If the reader acquires from this book but a fraction of the new knowledge which its author has done during its composition, then our efforts will be adequately rewarded. Manchester, July 1969

J. B.

BIRKS

Contents 1. Excited states of aromatic molecules

1.1 1.2 1.3 1.4 1.5

Electronic structure Molecular structure The PFEO model . Selection rules Other theoretical models Tables 1.1-1.3 1.6 References .

1 3 4 8 10 11 28

2. Photophysical processes

29

2.1 2.2 2.3 2.4

Introduction Unimolecular processes. Biphotonic processes Bimolecular processes 2.5 Rate parameters Tables 2.1-2.5 2.6 References

30

32 34

36 38 43

3. Absorption

3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

Vibronic states Hot bands . The extinction coefficient The Born-Oppenheimer approximation The Einstein coefficients Transition moments Oscillator strengths The Franck-Condon principle Absorption spectra ix

44 46 46

47 48 50

51 52 54

Contents

x

3.10 Flash photolysis and S J - Sp absorption 3.11 Multiphotonic absorption Tables 3.1-3.7 3.12 References

58 62 70 82

4. Fluorescence

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12

The fluorescence spectrum The mirror symmetry relation The radiative lifetime The fluorescence parameters . Competing bimolecular processes Determination of fluorescence lifetimes Determination of fluorescence spectra and quantum yields. Experimental tests of the radiative lifetime relations Fluorescence lifetimes and quantum efficiencies Fluorescence spectra Scintillator solutes Influence of environment on fluorescence and absorption spectra Tables 4.1-4.9 4.13 References .

84 85 87 88 90 94 97 100 103 106 108 109 120 139

5. ;Radiationless transitions

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15

Singlet-singlet internal conversion 142 Intersystem crossing 144 Triplet-triplet internal conversion 145 Internal quenching of fluorescence 145 TJ-Sointersystemcrossing . 147 The theory of radiationless transitions 149 T J - So intersystem crossing: Franck-Condon factors 152 The isotope rule . 155 TJ-S o intersystem crossing: comparison of theory with experiment . 156 Energy gaps 159 SJ - So internal conversion 160 SZ-SJ internal conversion 161 Dualluminescences 162 Internal conversion in benzene and its derivatives 171 Tables 5.1-5 .10 178 References . 191

Contents

6. The triplet state 6.1 Triplet and phosphorescence parameters . 6.2 The determination of triplet quantum yields 6.3 Triplet quantum yields . 6.4 Spectrophosphorimetry 6.5 The determination of phosphorescence quantum efficiencies 6.6 Phosphorescence lifetimes, quantum efficiencies and spectra 6.7 The heavy atom effect 6.8 Singlet-triplet absorption 6.9 Triplet-triplet absorption 6.10 Triplet energy levels 6.11 Assignment of the electronic states of the polyacenes 6.12 Spin-orbit interaction 6.13 Singlet-triplet intersystem crossing. 6.14 Triplet-triplet internal conversion and fluorescence 6.15 Photo-ionization . 6.16 Vapours of benzene and its derivatives 6.17 The triplet state of benzene Tables 6.1-6.23 6.18 References

xi

193 195 200 201 206 207 208 211 218 222 224 226 229 235 237 240 248 251 297

7. Excimers 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18

Excimer fluorescence Photostationary reaction kinetics Transient reaction kinetics Determination of rate parameters High temperature behaviour . Frequency factors and activation energies Diffusion-controlled processes Excimer fluorescence in solution Excimer fluorescence of crystals Photodimer and excimer formation. Sandwich dimers . Intramolecular excimer fluorescence The excimer potential energy diagram Theory of excimer states Determination of excimer interaction potential Photophysical processes in excimers Excimer formation processes. Excimer phosphorescence Tables 7.1- 7.11 7.19 References .

301 302 304 305 309 311 312 316 317 319 322 323 325 327 331 335 339 343 349 370

xii

Contents

8. Delayed luminescence 8.1 Types of delayed luminescence 8.2 E-type delayed fluorescence . 8.3 Fluorescence of mixed molecular species . 8.4 Triplet-triplet interaction in concentrated fluid solutions 8.5 Triplet-triplet interaction in dilute fluid solutions 8.6 P-type delayed fluorescence in fluid solutions 8.7 P-type delayed fluorescence in rigid solutions . 8.8 Mechanism of triplet-triplet interaction . 8.9 The determination of total triplet quantum yields 8.10 Recombination luminescence. Table 8.1 8.11 References .

372 373 375 378 384 385 389 ·391 394 397 400 401

9. Molecular complexes and exciplexes 9.1 Donor-acceptor complexes 9.2 Charge-transfer absorption 9.3 Kinetics ofDA complexes 9.4 Contact CT absorption . 9.5 Luminescence ofDA complexes 9.6 Exciplexes . 9.7 Mixed exci'mers 9.8 Fluorescence of exciplexes 9.9 Impurity quenching of fluorescence . 9.1 0 Photochemical quenching of fluorescence 9.11 Kinetics of impurity quenching 9.12 Impurity quenching of triplet states Tables 9.1-9.27 9.13 References .

403 406 410 412 415 420 421 425 433 439 441 447 452 489

10. Interactions with oxygen and nitric oxide 10.1 Oxygen and nitric oxide 10.2 Contact CT absorption. 10.3 Enhanced So - T I absorption . 10.4 Quenching by oxygen . 10.5 Photoperoxidation studies 10.6 Quenching by nitric oxide 10.7 Static quenching . 10.8 Kinetics of fluorescence quenching by oxygen 10.9 Collisional and exchange quenching Tables 10.1-10.3 10.10 References .

492 493 494 496 502 504 506 508 510 514 517

Contents

xiii

11. Energy migration and transfer 11.1 11.2 11.3 11.4 11.5 11.6 11 .7 11.8 11 .9 11.10 11.11 11.12 11 .13 11.14 11.15

Migration and transfer processes Radiative migration and transfer Exciton states in crystals Singlet exciton migration and transfer in crystals Triplet-triplet energy transfer in solution Triplet exciton migration and transfer in mixed crystals Triplet-triplet interactions in mixed crystals Triplet excitons in pure crystals Singlet-singlet energy transfer in solution. Influence of diffusion on energy transfer. Excitation migration and transfer in aromatic liquid solutions . Other intermolecular transfer processes Intramolecular energy transfer Photochemistry and photobiology Tables 11.1-11.18 References

12. Postscript Tables 12.1-12.2 References . Table Index of Compounds Table Index of Processes and Parameters

518 521 523 528 537 544 550 559 567 576 580 590 594 599 601 619 625 637 639 641 660

Author Index

669

Subject Index

681

1 Excited states of aromatic molecules 1.1 Electronic structure

The number 6 features in many of the properties of carbon. Carbon has an atomic number Z = 6; the nucleus of its most abundant isotope CI2 contains 6 protons and 6 neutrons; the crystal structure of graphite consists of parallel planes in which the carbon atoms are arranged in a regular hexagonal pattern; and the molecular structure of benzene is a similar planar regular hexagon, with the 6 carbon atoms at the corners of the hexagon bonded to the 6 hydrogen atoms. The electronic configuration of the ground state of the C atom is Is22s22p2. In forming compounds, one of the 2s electrons is considered to be excited to a 2p state, so that the electronic configuration of a C atom 'prepared for binding' is Is22s2p 3. The four valence electrons (2s2p 3) may take up three alternative configurations in forming molecules, corresponding to valences of 4 (e.g. CH 4 methane), 3 (e.g. C 2 H 4 ethylene, C6H6 benzene), or 2 (e.g. C 2 H 2 acetylene). In the first configuration, known as tetragonal or Sp3 hybridization, the four electron orbitals combine to produce four equivalent hybrid orbitals directed towards the corners of a regular tetrahedron centred on the C nucleus. These four equivalent electron orbitals associate with those of other atoms to give a saturated molecule, such as methane (CH 4 ). In the second configuration, known as trigonal or Sp2 hybridization, one of the originalp-orbitals (say pz) is unchanged, and three equivalent hybrid orbitals are produced by mixing s, Px and Py. These three Sp2 hybrid orbitals lie in the same plane (the xy plane), and they are inclined at equal angles of 120° to each other. It is this configuration which provides the hexagonal ring structure of benzene and the polycyclic aromatic hydrocarbons. The hybrid orbitals, which are symmetrical about their bonding axes and about

2

Excited States of Aromatic Molecules 1.1

the molecular plane, are known as a-electrons, and the bonds are called a-bonds. In benzene the a Sp2 hybrid orbitals of C interact with each other and with the Is orbitals of H in the manner shown diagrammatically in Figure 1.1 to produce the localized C-C and C-H a-bonds. 1

Figure 1.1 The a-electron orbitals of benzene (after Coulson l ) The pz atomic orbital of each C atom is unchanged by the Sp2 hybridization. Its wavefunction is anti symmetric to reflection in the nodal xy molecular plane, and it is known as a 7T-electron. In benzene the six 7T atomic orbitals of C interact to produce C-C 7T-bonds, the additional stabilization

Figure 1.2 The 7T-electron molecular orbitals of benzene (after Coulson l ) energy reducing the C-C bond length from 1·54 A (in C 2 H 6 ) to 1·39 A (in benzene). Unlike the a-electrons, the 7T-electrons are delocalized; the six 7T atomic orbitals interact to form six delocalized 7T molecular orbitals, as shown diagrammatically in Figure 1.2.1 Similar systems of delocalized 7T-e1ectrons occur in other aromatic molecules. It is the excited states of

1.2 Molecular Structure

3

these 7T-electron systems and the various transitions and interactions of these excited states with which this book is primarily concerned. In the third configuration of the C atom, digonal or sp hybridization, two of the original p-orbitals (say Py and pz) are unchanged, and two equivalent hybrid a-orbitals are produced by mixing sand Px' These a-orbitals are directed at 180 to each other along the x-axis, which is the line formed by the intersection of the npdal planes of the two p-orbitals. This configuration occurs in the linear molecule, acetylene (H-C= C-H). Apart from the C-H and C-C a-bonds, the py and pz atomic orbitals (7T-orbitals) of each C atom are paired to produce two C-C 7T-bonds, thereby reducing the C-C bond length from 1·54 A (in C 2 H 6) and 1-34 A (in C 2 H 4) to 1·20 A (in C 2 H 2). 0

1.2 Molecular structure The art of the organic chemist has led to the synthesis of a vast number of aromatic hydrocarbons, and the reader is referred to Clar's standard treatise 2 for details of their preparation and properties. The molecular structure of fifty-eight unsubstituted condensed aromatic hydrocarbons is shown in Table 1.1. The nomenclature adopted is that of Clar, apart from a few alternative names in common use which are listed. Table 1.1 includes all the condensed aromatic hydrocarbons with 1, 2, 3 (two compounds), 4 (six compounds) and 5 (fifteen compounds) benzenoid rings, and a selection of compounds with 6 to 13 benzenoid rings. In the unsubstituted compounds the number of 7T-electrons is equal to the number of C atoms in the molecule. Code numbers for the compounds are introduced for ease of subsequent reference. The compounds fall into two broad groups: (a) The cata-condensed hydrocarbons (formula, C4n+2H2n+4, where n = number of benzenoid rings) in which no C atom belongs to more than 2 rings; and (b) The peri-condensed hydrocarbons in which some C atoms lie at the junction of 3 rings (Nos. 4.1, 5.1-5.3, 6.1-6.4, 6.11-6.14, 7.1, 7.3, 7.4, 8.1,8.3,8.4,8.5,9.1,9.3,10.1,10.2,11.1,13.1). Some of the compounds can be arranged into various series. (i) The linear series, benzene, naphthalene, anthracene, tetracene, pentacene, hexacene, etc., are known as the polyacenes or acenes. (ii) The series, benzene, phenanthrene, pentaphene, etc., formed by the angular fusion of pairs of benzene, naphthalene, etc. systems to benzene, are known as the symmetric polyphenes or phenes (n odd).

Excited States of Aromatic Molecules 1.3

4

(iii) The series, naphthalene, tetraphene, hexaphene, etc., formed by similar angular fusion to naphthalene, are known as the asymmetric phenes (n even). (iv) The series, benzene, naphthalene, phenanthrene, 3: 4-benzophenanthrene, 3: 4: 5: 6-dibenzophenanthrene and hexahelicene, in which the lines joining the centres of successive fused rings are at 120 to each other and trace out the sides of a large hexagon, form the series of helicenes. In 3: 4-benzophenanthrene and higher compounds, steric hindrance between the H atoms on the inside of the large hexagon distorts the ring system out of planarity, so that in hexahelicene the large hexagon forms the first loop of a spiral. In the higher compounds, heptahelicene (No. 7.2), octahelicene (No. 8.2) and nonahelicene (No. 9.2), the spiral continues; so that there is an overlap of 1,2 and 3 rings, respectively. 0

There are a large number of derivatives of the condensed aromatic hydrocarbons, formed by substitution of one or more of the hydrogen atoms by alkyl (methyl CH3 , ethyl C2 H s, propyl C 3 H 7 , etc.), phenyl (C 6 H s), halo (fluoro F, chloro CI, bromo Br, iodo I) or other groups. Table 1.2 shows the nomenclature of the substitution positions in the simpler (n ~ 4) aromatic hydrocarbons, and the code, structure and formula of the principal derivatives for which photophysical data are available. There are also a number of other aromatic molecules of photophysical interest. The code, structure and formula for these compounds are listed in Table 1.3. Table 4.7 shows the structure of various aromatic molecules used as scintillator solutes.

1.3 The PFEO model The perimeter free electron orbital (PFEO) model, introduced by Platt, 3 is a useful theoretical model for the classification of the 7T-electronic states of the cata-condensed hydrocarbons. It can also be applied to the pericondensed hydrocarbons. In the cala-condensed hydrocarbons every C atom (and every 7T-electron) is on the molecular periphery. In the PFEO model the 7T-orbitals are treated as orbitals of free electrons travelling in a one-dimensional loop around the molecular perimeter. Approximating the perimeter initially to a circle of circumference I, the electron orbital corresponds to a plane rotator, and its wavefunction rfi must satisfy the boundary condition

rfi(x) = rfi(x + I)

(1.1)

5

1.3 The PFEO Model

where x is measured along the perimeter. The corresponding solutions (eigenfunctions) of the Schrodinger equation are of the form

ifio = 0/1)1/ 2

(1.2)

(2//)1/2 cos (21TqX//)

(1.3)

ifiq2 = (2//)1/2 sin (21TQx/l)

0.4)

ifiq(

=

4-------------------------g

q

3

2

-·+--t-.*"~~t·~~i+--·-

_0

t~.~,---IfF--·-----+-~.---

------ l,- -

-·+--t-.o-t--~~t.~~l-.o - -+--t

d

Figure 1.3 The perimeter free-electron

orbital model. The 1T-electron orbital energy levels of anthracene (n = 3). Vertical arrows represent spin, and horizontal arrows represent orbital momentum The corresponding allowed energy levels (eigenvalues) are quadratically spaced (Figure 1.3) and are given by 2

E

Q h2

= q

2mf2

=

1·21

X

106 q 2W

(1.5)

(Q = 0, 1,2, ... , h = Planck's constant, m = electron mass, Eq in em-I, 1 in A). Since the electron has a spin of ±t, andean move either clockwise or anticlockwise around the perimeter, all the energy levels except the lowest, Eo, are doubly degenerate.

6

Excited States of Aromatic Molecules 1.3

q, which is called the orbital ring quantum number, is a measure of the angular momentum and it describes the number of nodes of the wavefunction. When the circular perimeter is distorted to conform to the molecular perimeter, and the periodic potential due to the C atoms is introduced, q no longer describes momentum, but it remains a good quantum number, since it still determines the number of nodes. If there are n rings in the molecule, there are a total of 2(2n + I) 7T-electrons, since each C atom contributes one 7T-electron. Hence in the ground state of an n-ringed molecule, the highest filled level or shell is that for q = n. This is illustrated for anthracene (n = 3) in Figure 1.3. Platt introduced the nomenclature e, f, g, h to describe the electron shells for which q = n - 1 n, n + 1, n + 2, respectively. The total ring quantum number Q of the multi-electron system is given by the algebraic sum oftheq's of the individual electrons. The nomenclature A, B, C is introduced to describe the states of the system with Q = 0, 1, 2, respectively, and K, L, M (not to be confused with the notation of atomic electron systems) to describe the states with Q = 2n, 2n + 1, 2n + 2, respectively. In the perimeter constant-potential approximation all the states except A are doubly degenerate, since the total momentum can be in either direction around the perimeter. The introduction of the periodic potential due to the C atoms removes this degeneracy, so that each state splits into two components represented by subscripts a and b, which are identified below. The ground state of the system, with the configuration 14, Q = 0, and the electron spins paired, is the singlet state 1A. When an electron is excited from Ito g (Llq = 1) the excited state of the system has the configuration 1 3 g and Q = (n + 1) ± n = 1 or (2n + 1). The excited state may be either triplet or singlet, depending on whether there is a spin reversal in the electronic transition or not. Hence there are eight possible excited states corresponding to the 1 3 g configuration: 1Ba, 1B b, 1La, 1L b, 3Ba, 3B b, 3La, 3Lb' Higher excited states occur when Llq = 2; 1,3Ca , b and 1, 3 M a, b' corresponding to the/ 3 h configuration; and 1. 3 Ca ,b and 1,3K a , b corresponding to the e314 g configuration. The 1 3 g states are, however, adequate to describe many of the excited states of interest. The nodes in the electronic wavefunction occur at planes of symmetry perpendicular to the molecular plane. The suffixes a and b refer to the two alternative positions for the nodes relative to the molecule: a, where the nodal planes bisect the C-C bonds; and b, where the nodal planes pass through the C atoms. b may be formed from a by the interchange of nodes and antinodes. Figure 1.4 shows the position of the nodal planes and the sign of the wavefunction in different regions for the states Ba, B b, La, Lb in anthracene. Each nodal plane cuts the molecule twice, so that for the

1.3 The PFEO Model

7

B states (Q = 1) there are 2 cuts, and for the L states (Q = 2n + 1) there are 2(2n + 1) cuts, which is equal to the number of C atoms and of C-C bonds. The Ba state corresponds to a strong dipole oscillation in the molecular plane, polarized perpendicular to the long molecular axis, while the Bb state corresponds to a strong oscillation, polarized parallel to this

+

--CCE)---

l '~

I

I

+

(:(IX) - -

'8,

Figure 1.4 The perimeter free-electron orbital model. Classification of the L., L b , B. and Bb states of anthracene axis. The La and Lb states correspond to weaker dipole oscillations with polarizations perpendicular and parallel to the long molecular axis, respectively. The lowest excited state in the polyacenes is the triplet state 3La. The lowest excited singlet state may be either ILb (benzene, naphthalene, phenanthrene, etc.) or ILa (anthracene and higher linear polyacenes). The two singlet states of high Q (ILa,b) lie below the two singlet states of low Q (IBa,b)' In benzene IBa and IBb are degenerate (=IB); in the other

8

Excited States of Aromatic Molecules 1.4

compounds they are split, with I Bb lying below I Ba in the linear polyacenes. The assignment of the higher triplet states will be discussed in §6.11. 1.4 Selection rnles

An electronic state is characterized by certain basic properties: its energy, its multiplicity, and its symmetry, which in centro-symmetric molecules includes the parity. The multiplicity, symmetry and parity lead to important selection rules which influence the probability of transitions between the different electronic states. Multiplicity. A condensed aromatic hydrocarbon contains an even number of electrons. In the unexcited molecule the electron spins are paired by the Pauli principle to give the ground electronic singlet state A) of the molecule. If a 7T-electron is excited without change of spin, the resultant excited electronic state of the molecule is a singlet state. If a 7T-electron is excited and its spin is reversed in the transition, the resultant excited electronic state of the molecule is a triplet state. The terms 'singlet' and 'triplet' refer to the multiplicity of the electronic state, which describes its degree of degeneracy in the absence of a perturbing magnetic field. The application of a magnetic field to the molecule does not affect a singlet state: it removes the degeneracy of a triplet state and splits it into three distinct Zeeman levels. Electric dipole transitions between electronic states of different multiplicity are spin-forbidden. This multiplicity selection rule has a major influence on photophysical processes in aromatic molecules. The intensity of an absorption transition from the singlet ground state I A to the first excited triplet state 3La is only ~ 10- 8 that of the spin-allowed absorption transition to the excited singlet state 1Lb' corresponding to a spin-forbiddenness factor 1M ~ 10 8 • The finite value of 1M is due to spin-orbit interaction, which couples the eigenfunctions of the singlet and triplet states. 4 As a result of this perturbation, small amounts of triplet wavefunctions are mixed with the singlet wavefunctions, and vice versa, and we thus obtain a small, but finite, singlet-triplet transition probability (§6.l2). The spin-orbit interaction in the aromatic hydrocarbons is small, because of the low atomic numbers of their constituent carbon and hydrogen atoms. The large value of 1M ~ 108 for the 3La - I A transition is also due to the large energy separation between the interacting states. There is increased spin-orbit coupling between higher excited singlet and triplet states, which are closer in energy, and this results in a decrease of 1M for transitions between these states. Spin-orbit coupling is also increased by the inclusion of 'heavy atoms' of higher atomic number into the molecules or into their environment (§6.7).

e

1.4 Selection Rules

9

Symmetry. Electric dipole transitions between electronic states of the same symmetry are forbidden, and this symmetry selection rule influences the probabilities of transitions between the different electronic states. On the PFEO model the symmetries of the ILb and ILa states are similar to that of the ground A) state, so that I A - I Lb and I A - I La electronic transitions are symmetry-forbidden. The symmetries of the I Bb and I B. states differ from that of the I A state, so that I A - I Bb and I A - I Ba transitions are symmetry-allowed. The intensity of the I A - I Lb absorption is observed (Chapter 3) to be _10-2 - 10-3 that of the I A - I Ba,b absorption, corresponding to a symmetry-forbiddenness factoris - 102 - 10 3 • For the I A - ILa absorption transition is - 10. The symmetry-forbidden ness factor is - 10 - 10 3 is finite because of the presence of molecular vibrations which modify the symmetry of the pure electronic state. s For example, the PFEO electronic states of benzene correspond to the following symmetry species:

e

Benzene: IA =

IA1g;

1,3Lb =

1,3 B

2u ;

1,3L.

= 1,3 B

lu ;

1,3 B = 1,3 E

lu

The only transitions from the IA lg ground state of benzene which are symmetry-allowed and polarized in the plane of the molecule are those to a state of overall symmetry E lu so that the IA - IB electronic transition is allowed. The first excited electronic singlet state ILb has B 2u symmetry. However, if this is combined with a vibrational state in which an e2g mode is excited, then the total symmetry of the vibronic (electronic + vibrational) state is E lu (B 2u ,e2g = Elu), In the gas phase the 0 - 0 absorption band, corresponding to the pure I All - I B 2u electronic transition, is not observed, since it is symmetry-forbidden. However, vibronic absorption bands associated with e21 vibrational modes are observed, since these are symmetryallowed. These E lu vibronic bands derive their intensity by coupling to the allowed I E lu B) electronic state. The I A - ILa absorption transition, which is also symmetry-forbidden, derives its vibration ally-induced intensity in a similar manner. Parity. The PFEO electronic states of naphthalene, anthracene and the higher polyacenes correspond to the following symmetry species:

e

Polyacenes: IA=IA , ; 1,3La = I,3B2u ; 1,3Bb =I,3B3u ; 1, 3K a 1,3C =I,3B ; lg a

1,3Lb =I,3B3u ; 1,3B a =I,3B2u =1.3Alg ; 1,3K lg b

=1, 3 B

1, 3C = b

I,3A

Ig

In centrally symmetric systems, the states are divided into those of 'even' (g =gerade) and 'odd' (u = ungerade) parity, depending on whether the

Excited States of Aromatic Molecules 1.5

10

electronic wavefunction is symmetric or anti symmetric with respect to reflection in the centre of gravity. The parity selection rule, which is a special case ofthe symmetry selection rule, is that electric dipole transitions between states of the same parity are forbidden. According to this selection rule, transitions from the even-parity ground state Ag) to excited electronic states of odd (u) parity are allowed, but those to excited electronic states of even (g) parity are forbidden. Hence the main absorption spectrum of the polyacenes is assigned to the spinallowed and parity-allowed transitions to the IL a •b and 1Ba •b states. Platt3 has assigned a relatively intense transition which is observed in the absorption spectra of the polyacenes between the allowed 1A_I Bb and 1A_I Ba transitions to the parity-forbidden 1A-I Cb transition. This assignment appears to be confirmed by recent observations of SI - Sp absorption spectra by nanosecond photolysis (§3.1O). It is probable that molecular vibrations and interactions with adjacent states distort the symmetry and parity of the higher excited electronic states. The first excited singlet and triplet states of the polyacenes are of odd (u) parity. Absorption transitions from these states to higher excited singlet and triplet states, respectively, of even (g) parity are allowed. The transient absorption spectra corresponding to these transitions, which can be observed by flash photolysis (§3.1O), provide a means of studying excited states of even (g) parity not readily seen in the normal absorption spectrum.

e

1.5 Other theoretical models Apart from the PFEO model, there is a vast literature on the quantum theory of the aromatic hydrocarbons and the excited states of their 7Telectron systems. The different theoretical approaches include the valencebond (VB) model, the extended Hiickel model, the linear combination of atomic orbitals (LCAO) model, and the PFEO model. Several recent books and reviews 6 - 11 have been devoted to various aspects of the subject, and the reader is referred to these for fuller details. Among the more useful calculations of the excited states of the polyacenes are those of Pariser, 1 2 which will be discussed in §6.11.

Excited States of Aromatic Molecules

11

Table 1.1 Condensed aromatic hydrocarbons

Code

Structure

Compound

Benzene

2

Naphthalene

3.1

Anthracene

3.2

Phenanthrene

4.1

Pyrene

4.2

Tetracene (Naphthacene)

4.3

1: 2-Benzanthracene (Tetraphene)

4.4

Chrysene

4.5

3 : 4-Benzophenanthrene

Formula

0

C6 H 6

CO

CloHS

CXD

C 14 H 1O

cx9

0 CCCO

ccx9

ox9 W

C 14 H 1O

C l6 HjQ

C l8H u

C I5 H 12

C l8 H u

C I8 H 12

Excited States of Aromatic Molecules

12

Table 1.1 (continued) Code

Compound

Structure

cxg

Formula

4.6

Triphenylene

5.1

Perylene

gg

C 2o H 12

5.2

1 : 2-Benzopyrene

{5D

C 2o H 12

5.3

3 : 4-Benzopyrene

5.4

Pentacene

5.5

1 : 2-Benzotetracene

5.61:2:3:4-Dibenzanthracene

059

cecco

cxxx9

C 1s H 12

C 2o H 12

C n H 14

C n H 14

&cited States of Aromatic Molecules

13

Table 1.1 (continued)

Code

Compound

5.7

1 :2:5:6-Dibenzanthracene

5.8

1 :2:7:8-Dibenzanthracene

5.9

Picene

5.10 1: 2-Benzochrysene (1 : 2: 3: 4-Dibenzophenanthrene)

5.11

5: 6-Benzochrysene (1 :2:5 :6-Dibenzophenanthrene)

5.12

1 :2-Benzotetraphene (2: 3 : 5: 6-Dibenzophenanthrene)

5.13

3:4-Benzotetraphene (2 : 3: 7: 8-Dibenzophenanthrene)

Structure

ox8 cxSXO

Formula

Cu H14

C 22 H 14

14

Excited States of Aromatic Molecules Table 1.1 (continued)

Code

Compound

Structure

Formula

5.14 3:4: 5: 6-Dibenzophenanthrene

5.15 Pentaphene

6.1

Anthanthrene

6.2

1: 12-Benzoperylene

6.3

1 : 2-Benzoperylene

6.4

2: 3-Benzoperylene

6.5

Hexacene

C n H 14

&X9

W ~

C22 H 12

C22 H 12

C 24 H 14

Excited States of Aromatic Molecules

15

Table 1.1 (continued)

Code

Compound

6.6

1: 2-Benzopentacene

6.7

Hexaphene

6.8

Hexahelicene

6.9

1: 2: 3 :4: 5: 6-Tribenzanthracene

6.10 Phenanthro-(3': 2': 2: 3)phenanthrene (l :2 :7:8-Dibenzotetracene)

6.11

1 :2:6:7-Dibenzopyrene

Structure

Formula

Excited States of Aromatic Molecules

16

Table 1.1 (continued)

Code

Compound

Structure

Formula

00

C 26 H 16

6.12 3:4:8:9-Dibenzopyrene

6.13 Naphtho-(2':3':3:4)pyrene

6.14

1 :2:3:4-Dibenzopyrene

6.15

1 : 2: 3: 4-Dibenzotetracene

6.16

1:2:3:4:5:6:7:8Tetrabenzonaphthalene(1 :2: 7: 8Dibenzochrysene)

7.1

Coronene

@

C 24 H 12

17

Excited States of Aromatic Molecules Table 1.1 (continued) Code

Compound

Structure

Formula

See §1.2

7.2

Heptahelicene

7.3

2: 3: 8:9-Dibenzoperylene

7.4

Phenanthro(3': 2': 3 :4)-pyrene

7.5

1:2:3:4:5:6:7:8Tetrabenzanthracene

8.1

Bisanthrene

m;

C18 H 14

8.2

Octahelicene

See § 1.2

C n H 20

8.3

Dinaphtho(2' :3':3:4)(2": 3": 9: lO)-pyrene

Excited States of Aromatic Molecules

18

Table 1.1 (continued)

Code

Compound

8.4

1 :2-Benzocoronene

8.5

1:12:2 :3:10:11Tribenzoperylene

9.1

1: 14-Benzobisanthrene

9.2

Nonahelicene

9.3

1:2:3:4:6:7:12 : 13Tetrabenzopentacene

10.1

Ovalene

Structure

See §1.2

Formula

19

Excited States of Aromatic Molecules Table 1.1 (continued) Code

Compound

10.2

1:2:3 :4:5:6:10 : 11Tetrabenzanthanthrene

11.1

5:6:8 :9:14:15:17 :18Tetrabenzoheptacene

13.1

1:12:2 :3:4:5:6:7:8: 9 : 10: 11-Hexabenzocoronene

2

Structure

Formula

20

Excited States of Aromatic Molecules Table 1.2 Nomenclature and structure of derivatives of condensed

aromatic hydrocarbons Code

Structure

Compound

60

Formula

I

1

Benzene

S

C6H 6

2 3

4

ld

C 6D 6

Benzene·d 6

IA

Toluene

lAd

Toluene·d B

IB

ortho-Xylene

IC

meta-Xylene

lD

para-Xylene

lDd

p-Xylene·d 1o

c5

C6 Hs.CH3 C6 Ds·CD3

CH 3

(r

CH 3

C 6 H 4 '(CH3h

CH 3

QCH'

Q CH 3

C6 H 4 ·(CH3h

C6 HdCH3)2

C6 D 4 '(CD 3h

CH 3

C 6 H 3 ·(CH3 )3 lE

Mesitylene

"'C6CH' H'CqCH' CH 3

IF

Hexamethylbenzene

H3C

CH3

CH 3

CdCH3 )6

21

Excited States of Aromatic Molecules Table 1.2 (continued) Code

IG

Structure

Compound

Formula

¢fCH'

1,2,4-Trimethyl benzene

C 6 H 3 ,(CH3h

CH 3 C 2H 5

lH

6

Ethyl benzene

C 6 H s,C2 H s

H H 3C,t.....- CH3

11

iso-Propyl benzene

C 6 H s,C3 H,

6

C 2H S

I

lJ

n-Propyl benzene

IK

Durene (l ,2,4,5-tetramethyl benzene)

(5 H3C

C 6 H s'C 3 H,

qCH'

C 6 H 2 ,(CH3)4

CH 3

IL 1M IN 10

l,4-Dichlorobenzene 1,3,5-Trichlorobenzene 1,2,4,5-Tetrachlorobenzene Hexachlorobenzene

C 6 H 4 Ch C 6 H 3 Ch C 6 H 2 CI 4 C 6 CI 4

2

Naphthalene (N)

1

'CO2 8

6

3

5

2d 2A 2B 2C 2D

Naphthalene,dB I-Methyl N 2-Methyl N 1,6-Dimethyl N 2,6-Dimethyl N

CIOHS

4

ClODs C lOH"CH 3 C lO H,'CH 3 C lO H 6 ,(CH3)2 C IOHdCH 3 )2

22

Excited States of Aromatic Molecules Table 1.2 (continued)

Code

Compound

2E 2F 2G 2H 21 2J 2K 2L 2M 2N 20 2P 2Q 2R 2S 2T 2U 2V 2W 2X 2Y

2,3-Dimethyl N 2,7-Dimethyl N 1,2-Dimethyl N 1,3-Dimethyl N 1,4-Dimethyl N 1,5-Dimethyl N 1,7-Dimethyl N 1,8-Dimethyl N 2,3,5-Trimethyl N I-Ethyl N 2-Ethyl N I-Fluoro N I-Chloro N I-Bromo N I-Iodo N 2-Fluoro N 2-Chloro N 2-Bromo N 2-lodo N I-Methoxy N 2-MethoxyN

2Z

Acenaphthene

2Zd

Acenaphthene,d iO

3,1

Anthracene (A)

Structure

C lo HdCH 3 )2 C iO H 6 -(CH 3 h C iO HdCH 3 h C iO HdCH 3 h C IO H 6 '(CH 3 h C iO HdCH 3 h C lo HdCH 3 )2 C iO HdCH 3 )2 C lo H s '(CH 3 )2 C iO H 7'C 2 H s C iO H 7'C2 H s CiO H 7'F C IO H 7'CI CiOH 7'Br CiOH 7'I CiOH.j'F C IO H 7'CI CiOH 7'Br C IO H 7'I C iO H 7'OCH 3 C iO H 7,OCH3

05 8

9

Anthracene,d lo 9-Methyl A 9-Methyl A ,d 12 9,lO-Dimethyl A

3,lC

9,lO-Diphenyl A

3.1D

9-Phenyl A

C l2 H iO C l2 D iO 1

'CX:CY

6

3,ld 3.1A 3.1Ad 3,1B

Formula

3

s

10

C I4 H iO C I4 D iO C 14 H 9 ,CH3 C 14D 9 ,CD 3 C 14 HdCH 3 h

23

Excited States of Aromatic Molecules Table 1.2 (continued) Code 3.1E 3.1F 3.1G 3.1H 3.11

Structure

Compound

Formula C 14 H 9 ·C2 H s C 14 H 9 ·C3 H 7 C 14 HdC 3 H 7)2 C 14 H s ·CI 2 C 14 H 9 ·OCH 3

9-Ethyl A 9-n-Propyl A 9,lO-Di-n-propyl A 9,IO-Dichloro A 9-Methoxy A CH 3

3.1J

9-Methyl, lO-methoxy A

3.1K 3.1L

9-Acetoxy A 9-Anthracene carboxylic acid 9-Cyano A i-Chloro A

3.1M 3.IN

«0

C 14 H s ·CH3 ·OCH3

OC H 3

C I4 H 9 ·COOCH3 C I4 H 9 ·COOH C I4 H 9 ·CN C I4 H 9 ·Cl

3

3.2

69'

Phenanthrene

5

:

3.2d

Phenanthrene·d lO

4.1

Pyrene (P)

C 14 H Io

1

10

9

C 14 D IO

9

7 6

0 5

I

C I6 H iO

2

3

4

4.1d 4.lA 4.1B 4.lC 4.10 4.lE 4.1F 4.IG 4.1H

pyrene·d lO I-Methyl P 3-Methyl P 4-Methyl P 3-Chloro P 3-Bromo P 3-Cyano P 3-Pyrene sulphonate 3,5,8,IO-Pyrene tetrasulphonate

4.2

Tetracene

10

II

12

C I6 D Io C I6 H 9 ·CH3 C I6 H 9 ·CH3 C I6 H 9 ·CH3 C I6 H 9 ·CI C I6 H 9 ·Br C I6 H 9 ·CN C I 6 H 9 ·S03 Na C I 6 H 6 ·(S03 Na)4 1

90):))2 8 3 7

6

5

4

C Is H 12

24

Excited States of Aromatic Molecules Table 1.2 (continued)

Code 4.2d

Compound

Structure

Formula

Tetracene·d\2

C 1sD\2

2'

4.3

t : 2-Benzanthracene (BA)

4.3d 4.3A 4.3B 4.3C 4.3D 4.3E 4.3F 4.3G 4.3H 4.31 4.3J 4.3K 4.3L 4.3M 4.3N 4.30 4.3P 4.3Q 4.3R 4.3S 4.3T 4.3U

BA·d\2 I '-Methyl BA 2'-Methyl BA 3'-Methyl BA 4'-Methyl BA 3-Methyl BA 4-Methyl BA 5-Methyl BA 6-Methyl BA 7-Methyl BA 8-Methyl BA 9-Methyl BA to-Methyl BA 2',4-Dimethyl BA 2',6-Dimethyl BA 9,1O-Dimethyl BA 3',6-Dimethyl BA 5-Ethyl BA 5-n-Propyl BA 5-Butyl BA 5-AmyIBA 6-iso-Propyl BA

4.3V

Cholanthrene

7 6

exXS?' 8

9

5

10

:'

C 1s H\2

3

4

y:p

C 1s D i2 C 1s H ll ·CH3 ClsHII·CH3 C 1S H ll ·CH3 C 1s H ll ·CH3 C 1s H ll ·CH3 C I8 H ll ·CH3 C 1s H ll ·CH3 C 1sH ll ·CH3 C 1s H ll ·CH3 C 1s H ll ·CH3 C 1S H ll ·CH 3 C 1s H ll ·CH3 C ls H iO ·(CH3)2 ClsHIO·(CH3)2 C ls H iO ·(CH3)2 C lsH iO ·(CH3h ClsHll,C2Hs ClsHll,C3H7 CISHll,C4H9 C1sH ll .CSHll Cl sHll,C3H7

C 20 H 14

H 2 C-CH z

4.3W

20-Methyl cholanthrene

C20H13'CH3 H)C H 2C-CHz

25

Excited States of Aromatic Molecules Table 1.2 (continued)

Code

Structure

Compound

Eormula 5

w' 7

4.4

3

s

Chrysene

C18 H 12

1

9

4.4d

Chrysene·d 12

10

1

12

II

C Is D 12

3'

2

4.5

3: 4-Benzophenanthrene (BP)

C 1sH 12 9

4.5d 4.5A 4.5B 4.5C 4.5D 4.5E 4.5F

4.6

Bp·d 12 I-Methyl BP 2-Methyl BP 5-Methyl BP 6-Methyl BP 7-Methyl BP 8-Methyl BP 10

Triphenylene

7

6

~H S

12

,

I

4

4.6d

C 1sD 12 C 1s H l l ·CH3 C 1s H l l ·CH3 C 1s H l l ·CH3 C 1s H l l 'CH3 C 1s H l l 'CH3 ClsHII·CH3

Triphenylene·d 12

C 1s H 12

2

C 1sD 12

Excited States of Aromatic Molecules

26

Table 1.3 Other aromatic molecules

Code

Compound

A

Biphenyl

Ad

Biphenyl-d lO

B

Fluorene

Structure

Formula

0-0

C 12 R IO

QO

C l3 R IO

C l2 D IO

Hz

era

C

Biphenylene

D

para-Terphenyl

Dd

p- Terphenyl-d l4

C Is D J4

E

para-Quaterphenyl

C 24 R I8

F

Fluoranthene

G

Azulene

Gd

Azulene-d s

H

Rubrene

J

meta-Terphenyl

0-0-0

£ «)

C l2 R s C Is R J4

C I8 R IO

CIORs CIO D 8

27

Excited States of Aromatic Molecules Table 1.3 (continued)

Code

Compound

K

1,3,5-Triphenyl benzene

L

ortho-Terphenyl

M

trans-Stilbene

Structure

~ Q-CCH)2-D

Formula

C 18 H 14

C 14 H Il

0

N

Benzophenone

Q-~-D

C 13 H IO O

28

Excited States of Aromatic Molecules 1.6

1.6 References 1. C. A. Coulson, Valence, Oxford University Press, Oxford, 1952. 2. E. C1ar, Polycyclic Hydrocarbons, Academic Press, London, New York; Springer-Verlag, Berlin, 1964. 3. J. R. Platt, J. Chern. Phys., 17, 484 (1949). 4. H. F. Hameka, The Triplet State, Cambridge University Press, Cambridge, p. 1,1967. 5. J. N. Murrell and J. A. Pople, Proc. Phys. Soc. A, 69, 245 (1956). 6. M. Kotani, K. Ohno and K. Kayama, Encyclopaedia 0/ Physics, SpringerVerlag, Berlin, Vol. 37/2, p. 1, 1961. 7. J. R. Platt, Encyclopaedia 0/ Physics, Springer-Verlag, Berlin, Vol. 37/2, p. 173, 1961. 8. J. N. Murrell, The Theory 0/ the Electronic Spectra 0/ Organic Molecules, Methuen, London, 1963. 9. J. R. Platt and co-workers, Systematics 0/ the Electronic Spectra o/Conjugated Molecules, Wiley, New York, 1964. 10. P. O. Lowdin and B. Pullman (Eds.), Molecular Orbitals in Chemistry, PhysiCS and Biology, Academic Press, New York, London, 1964. 11. R. L. Flurry, Molecular Orbital Theories 0/ Bonding in Organic Molecules, Arnold, London; Dekker, New York, 1968. 12. R. Pariser, J. Chern. Phys., 24, 250 (1956).

2 Photophysical processes 2.1 Introduction

A photophysical process is defined as a physical process (i.e. one which does not involve a chemical change) resulting from the electronic excitation of a molecule or system of molecules by non-ionizing electromagnetic radiation (photons). The photophysics of organic molecules is relevant to their photochemistry and to photobiology (§11.14), although photochemical processes will only be referred to en passant. Photophysical processes also occur following the excitation of an organic molecular system by ionizing radiation. The relation of these processes to the radiation physics and to the scintillation mechanism in such systems has been discussed elsewhere! (§11.11). The radiation physics of organic molecular systems is relevant to their radiation chemistry and to radiation biology. Recent studies have also been made of the excitation of aromatic molecules by non-ionizing electron beams, and the connection between such electron excitation and photon excitation has been discussed, with particular reference to benzene and naphthalene 2 (§6.8). We shall mainly deal with the photophysical processes which occur in the condensed aromatic hydrocarbons and their simple derivatives. This group of compounds has been studied in most detail, though many of the processes considered are common to other aromatic compounds. To generalize the discussion, we introduce the following simple notation for the electronic states. So SJ

Sp (p > 1)

TJ Tq(q > 1)

ground singlet state first excited singlet state higher excited singlet states first excited triplet state higher excited triplet states

Photophysical Processes 2.2

30

1M 1M* 1M** 3M* 3M**

molecule in So molecule in SI molecule in Sp molecule in T 1 molecule in T q

The singlet states, together with their associated vibrational levels (Chapter 3) constitute the singlet manifold. The triplet states, together with their associated vibrational levels, constitute the triplet manifold (Figure 2.1).

iv

x

xi

I I I I I

' ~~i

.......... I

I I I

xii

~

S,

\~==~- -, I

: I

I I I I i

V

I

, XIV

'

\

I

, \

I

~

....

I I

xiiil vii

I

I I I I

, I

I

So

iii ix

I

vi

xv i viii I (?)

ii

I I

...

Figure 2.1 Unimolecular photophysical processes. Solid lines, radiative transitions; broken lines, radiationless transitions 2.2 Unimolecular processes

The unimolecular photophysical processes that can occur in an isolated molecule in the vapour phase at low pressure, or in dilute solution in a transparent medium, can be divided into the following categories. (a) Radiative ex citation (absorption) transitions in which the molecule is excited from a lower to a higher electronic state by the absorption of a photon.

2.2 Unimolecular Processes

31

(b) Radiative de-excitation (luminescence) transitions in which the molecule is de-excited from a higher to a lower electronic state by the emission of a photon. A radiative transition between states of the same multiplicity is described as fluorescence. A radiative transition between states of different multiplicity is described as phosphorescence. (c) Radiationless transitions between isoenergetic vibrational levels of different electronic states. Such transitions are normally preceded by radiationless thermal activation of the initial electronic state, and/or followed by radiationless thermal de-activation of the final electronic state (Chapter 5). A radiationless transition between states of the same multiplicity is described as internal conversion. One between states of different multiplicity is described as intersystem crossing. lbsorption transitions

(i) So - Sl and So - Sp absorption is spin-allowed, and it corresponds to the main electronic absorption spectrum (Chapter 3). (ii) So - Tl and So - Tq absorption is spin-forbidden, but it can be observed by using long light paths, intense light sources, or perturbation methods (§6.8). (iii) Tl - Tq absorption is commonly observed by flash photolysis (§6.9). Tl is populated by intersystem crossing [see (xiv) below] from Sl> which is initially excited by an intense light flash. The transient absorption is observed during the T 1 excitation lifetime. (iv) Sl - Sp absorption is observed by nanosecond flash photolysis (§3.1O). Sl is initially populated by an intense light flash of very short duration, and the transient absorption is observed during the Sl excitation lifetime. Luminescence transitions

(v) Sl - So fluorescence of short duration (~1 - 10 3 ns) corresponds to the normal fluorescence emission (Chapter 4). (vi) Tl - So phosphorescence generally occurs, but it is of longer duration (~l - 104 ms) than the fluorescence, because it is a spin-forbidden transition (Chapter 6). (vii) Sp - So fluorescence has been observed in a few compounds, notably azulene (§5.13). (viii) Tq - So phosphorescence has been reported in fluoranthene and a few other compounds (§5.l3), but it is a very improbable process. (ix) Tq - Tl fluorescence corresponding to the inverse of the Tl - Tq absorption (iii), has been reported in azulene and naphthalene (§6.14).

32

Photophysical Processes 2.3

(x) Sp - SI fluorescence, the inverse of (iv), is a possible process, yet to be observed. Radiationless transitions (Chapter 5) (xi) S2 - SI and Sp - Sp_1 internal conversion usually occurs rapidly. This

accounts for the negligible yield of Sp - So fluorescence from most molecules. (xii) T2 - TI and Tq - Tq_1 internal conversion is usually rapid, and this accounts for the negligible yield of T q - So phosphorescence from most molecules. (xiii) SI - So internal conversion to the ground state, and (xiv) SI - TI and SI - Tq intersystem crossing constitute the internal quenching of Sl> which competes with the normal fluorescence (v). (xv) TI - So intersystem crossing competes with the normal phosphorescence (vi). (xvi) TI - SI intersystem crossing may occur by thermal activation of TI during its excitation lifetime to a vibrational level isoenergetic with S I' This process leads to E-type (eosin-type) delayedfluorescence, which has the same spectrum as the normal fluorescence (v), but different temperature and time characteristics (§8.2). (xvii) Sp - Tq intersystem crossing from higher excited singlet states (iM**) has been observed in some compounds (§6.I3). These various unimolecular processes, which are shown diagrammatically in Figure 2.1, and enumerated in Table 2.1, are discussed more fully in subsequent chapters. 2.3 Biphotonic processes

When the molecular system is irradiated by an intense light source (e.g. a laser beam), additional biphotonic processes can occur, corresponding to the absorption of two photons by the same molecule. The two photons may be of the same or different energies, and they may be absorbed at the same time or at different times. Three pairs of the processes already considered are biphotonic in nature, namely (a) TI - Tq absorption (iii), following So - SI absorption (i) and SI - TI intersystem crossing; (b) TI - Tq absorption (iii), following So - TI absorption (ii); and (c) SI - Sp absorption (iv), following So - SI absorption (i). The photons used to study the transient TI - Tq and SI - Sp

2.3 Biphotonic Processes

33

absorptions normally differ in energy from those used for the initial excitation. However, with intense monochromatic beams the corresponding biphotonic processes can occur: (xviii) So - SI absorption, followed by SI - TI intersystem crossing, and TI - Tq absorption, i.e. 1M + hv --+ IM* --+ 3M *} 3M* + hv --+ 3M** I -----

(2.1)

~-------~----'--'

Sp---""""'+---

S1-~~-L....L...-..--,

"-

"-

"-

x·~~-~-~~T1

so-L--L---L-------L-----

Figure 2.2 Biphotonic photophysical processes. al a2; b l b 2 ; CI C2; d l d 2 • I = ionization potential (xix) So - TI absorption followed by TI - Tq absorption, i.e. 1M + hv --+ 3M* } 3M* + hv --+ 3M**

(2.2)

(xx) So - SI absorption followed by SI - Sp absorption, i.e. 1M + hv --+ 1M* } IM* + hv --+ IM**

(2.3)

34

Photophysicaj Processes 2.4

The energy of the higher excited state (3M**, IM**) thus produced by the biphotonic process may exceed the molecular ionization energy, so that the following processes may occur (§6.15). (xxi) Biphotonic ionization via T 1 , i.e. (xviii) or (xix), followed by

(2.4) (xxii) Biphotonic ionization via Sl' i.e. (xx), followed by I

M**

-i>-

2M+ + 2e-

(2.5)

A further biphotonic process which has been observed with laser beam excitation is (xxiii) So - Sp double-photon excitation, produced by the simultaneous absorption of two photons, each of energy less than Sl> by the same molecule (§3.11). These various biphotonic processes are shown diagrammatically in Figure 2.2.

2.4 Bimolecular processes The photophysical processes so far enumerated can all occur in isolated molecules. Additional processes occur in concentrated or aggregated systems due to interactions with molecules of the same species, or in mixed molecular systems due to interactions with molecules of a different species. Interactions between two molecules of the same species are referred to as homopolar bimolecular processes. Interactions between two molecules of different species are referred to as heteropolar bimolecular processes. The various bimolecular processes can be divided into five broad types: (a) perturbation processes; (b) excitation migration and transfer processes; (c) complex formation by two unexcited molecules; (d) complex formation by an excited molecule and an unexcited molecule; and (e) interaction between two excited molecules. We shall enumerate some representative examples of €ach type of interaction. (a) Interaction with an adjacent molecule (or molecules) may perturb the energy levels of the excited aromatic hydrocarbon molecule, and modify its photophysical properties and behaviour. The Davydov splitting which modifies the absorption characteristics of an aromatic crystal can be considered as a homopolar perturbation process (§11.3). The enhancement

2.4 Bimolecular Processes

35

of intersystem crossing produced by interactions with paramagnetic molecules (e.g. oxygen) (§10.4) or molecules containing atoms of high atomic number (external heavy-atom effect) (§6.7) are examples of heteropolar perturbation processes. (b) The interaction of an excited molecule with an unexcited molecule can lead to the transfer of its excitation energy either by a radiative process (emission followed by absorption) or by a radiationless process. Homopolar excitation transfer between molecules of the same species is referred to as excitation migration. In a homopolar aromatic crystal such excitation migration, known as exciton migration, leads to a delocalization of the IM* and 3M* excitation. Heteropolar radiative and radiationless transfer . between aromatic molecules of different species occurs under appropriate conditions, and it is referred to as excitation (or energy) transfer. The various types of excitation migration and transfer processes, which are listed in Table 2.2, are discussed in Chapter 11. (c) Aromatic hydrocarbon molecules do not normally associate in the ground state, although homopolar molecular complexes are often formed between dye molecules in concentrated solutions. Heteropolar donoracceptor complexes are, however, formed between aromatic hydrocarbons and other appropriate molecules (e.g. p-chloranil) in the ground state, and the photophysica1 properties of these complexes, which may be fluorescent and/or phosphorescent, differ from those of their constituent molecules (Chapter 9). (d) Many aromatic hydrocarbon molecules in their first excited singlet of the same species, state M*) interact with unexcited molecules

e

eM)

(2.6)

e

to produce excited dimers D*), which are dissociated in the ground state. These homopolar excited dimeric complexes are known as excimers. The excimer behaves like a distinct molecular species, and it exhibits its own characteristic fluorescence and other photophysical properties (Chapter 7). Similar heteropolar excited molecular complexes, also dissociated in the ground state, and known as exciplexes, are produced by the interaction of IM* with unexcited molecules of other aromatic hydrocarbons, or with unexcited molecules eQ) of other appropriate compounds, (2.7) Exciplexes exhibit their own characteristic fluorescence and other photophysical properties (Chapter 9). (e) The final type of bimolecular process to be considered is that between two excited molecules. The simplest process of this type to be observed

Photophysical Processes 2.5

36

is the homopolar interaction between two identical molecules each in the excited triplet state eM*), 3M* + 3M*

,If ID*

(2.8) '" IM* + 1M

The triplet-triplet association process in fluid solution yields both excited molecules M*) and excimers D*), and the fluorescence of these entities constitutes the P-type (pyrene-type) delayed fluorescence of the system (Chapter 8). The various homopolar and heteropolar bimolecular interactions are listed in Tables 2.3 and 2.4, respectively, together with the photophysical processes in the resultant excimers and exciplexes.

e

e

2.5 Rate parameters The probability of a unimolecular process is independent of time t, and it is expressed as a first-order rate parameter kx, measured in S-I. If a molar concentration [X*] moles/litre of an excited molecular species X* decays by a unimolecular process of rate parameter kx, the rate of decay of [X*] is _ d[X*] dt

=

kx[X*)

(2.9)

If a molar concentration [X*) of an excited species X* decays by a bimolecular process with a second-order rate parameter k yx (measured in M- I S-I), due to interaction with another species Y of molar concentration [Y), the rate of decay of [X*) is - d[X*) dt

=

kyx[Y) [X*)

(2.10)

When k yx is independent of t, the system is said to obey Stern-Volmer kinetics. Stern-Volmer kinetic behaviour was originally observed for bimolecular collisional quenching in gases, and it is also normally valid for bimolecular collisional processes in fluid solutions, for quenching and energy transfer processes in low-viscosity fluid solutions, where efficient molecular diffusion occurs, and for quenching and energy transfer processes in aromatic liquids and crystals, where efficient excitation migration occurs. Stern-Volmer kinetics do not apply to energy transfer or other bimolecular interactions in viscous or rigid solutions, in which molecular diffusion and excitation migration is inhibited. This type of behaviour, in which k yx is not independent of t, will be considered in Chapter 11. InitiaIIy we shall restrict the discussion to systems in which Stern-Volmer kinetics are applicable.

2.5 Rate Parameters

37

In considering the reaction kinetics of various photophysical processes, we shall adopt the rate parameter notation introduced by Birks et al. 3 In this notation the rate parameter kBA describes the B +-- A process, in which A is the original excited molecular species, and B is the product radiation, product species or interacting species. The total rate parameter kA is the sum 2 k jA of all the unimolecular processes, other than dissociation, operatj

ing on the excited species A. The suffix notation used is as follows:

M = IM*; D=ID*; E=IE*; T = 3M*; N =3D*; X = 3E*; H = IM**; J = ID**; K = 3M**; G = ground state; Y (or Z) = acceptor molecule; Q = quencher molecule; F = fluorescence; P = phosphorescence; I = internal quenching; TT = 3M*+3M* The more important rate parameters are listed in Table 2.5 for ease of reference. Molar concentrations are represented by square brackets. The first-order rate parameters are indicated by single parameters, e.g. k FM • The second-order rate parameters are shown multiplied by the molar concentration of the interacting species, e.g. kQM[Q], to express the two types of parameters in common units of S- I .

38

Photophysical Processes Table 2.1 Unimolecular photophysical processes

Process

Rate parameter

Description

Ref.

, M processes

'M + hv -;. 'M* 'M + hv-;.'M** 'M + hv -;.2 M++ 2e'M + 2hv -;. 'M* ' M + hv -;.3 M * 'M + hv -;.3 M**

So - S, absorption (i) So - Sp absorption (i) Photo ionization Biphotonic absorption (xxiii) So - T , absorption (ii) So - T q absorption (ii)

, M * processes 'M* -;.'M + hVM 'M* -;. 'M 'M*-;.3M* 'M* -;.3M** 'M* + hv -;. 'M** 'M* +hv -;. 2M+ + 2e-

S, - So fluorescence (v) kFM Chap. 4 S, - So internal conversion (xiii) kGM} §5.11 S, - T, intersystem crossing (xiv) k kiM Sl - T q intersystem crossing (xiv) J ™ §6.13 S, - Sp absorption (iv) §3.1O S, photo ionization (xxii) §6.15

'M** processes IM** -;.'M* 1 M ** -;. , M + hVH 'M** -;. 3M** 'M**-;.'M

Sp - S, internal conversion (xi) Sp - So fluorescence (x) Sp -;. T q intersystem crossing (xvii) Sp - So internal conversion

3M* processes 3M* -;.'M + hvp 3M*-;.'M 3M*-;.'M* 3M* + hv -;. 3M** 3M* + hv-;. 2M* + 2e -

T, - So phosphorescence (vi) Tl - So intersystem crossing (xv) Tl - S, intersystem crossing (xvi) T 1 - T q absorption (iii) T, photoionization (xxi)

3M** processes 3M** -;.3M* 3M** -;. 3M + hv 3M** -;.'M* 3M**-+3M* + hv

Tq Tq Tq Tq -

Chap. 3 Chap. 3 §§6.15, 9.2 §3.11 §6.8 §6.8

1

T I internal conversion (xii) So phosphorescence (?) (viii) S, intersystem crossing (xvi) T, fluorescence (ix)

kMH kFH kTH kGH

§5.12 §5.13 §6.13 §5.14

kPT

Chap. 6

kGT kMT

§5.5 if. §8.2 §6.9 §6.15

kTK

§6.14 §5.13 §6.14 §5.13

kpK

kMK kFK

39

Photo physical Processes Table 2.2 Excitation migration and

transfer processes (see Chapter 11) Migration IM* + IM ""IM+IM* 3M*+IM "" IM+3M* 3M* + 3M* "" IM+IM* 3M* + 3M*....,.. 1M + 3M** IM* + 3M*....,.. 1M + 3M** Transfer IM* + ly....,..IM + ly* 3M* + Iy ....,.. 1M + 3y* 3M*+ly ....,..IM+ly* 3M* + 3y*....,.. 1M + Iy* 3M* + 3y* ....,.. 1M + 3y** IM* + 3y* ....,.. 1M + 3y**

40

Photophysical Processes Table 2.3 Homopolar bimolecular interactions and excimer processes (see Chapters 7 and 8)

Process

Description

Interactions M* + 1M -+ 1D* Singlet excimer formation Triplet excimer formation 3M* + 1M -+3D* 3M* + 3M*-+1M* + 1M 3M* + 3M* -+ 1D* 3M* + 3M* -+3D* L ' . . . 3M* + 3M* -+ 5D* r Tnplet-tnplet mteractions 3M* + 3M* -+ 2M+ + 2M3M* + 3M* -+1M+3M** 2M+ + 2M--+ 1M* + 1M} 2M++2M- -+ 1D* Cation-anion association 2M++ 2M- -+ 3M* +1 M 2M+ + 2M- -+ 3D* 1M** + 1M-+1D** 1D** formation 3M** + 1M-+3D** 3D** formation 1M* + 1M* -+2M++ 2M- Singlet-singlet interaction 1M* + 1M -+3M* + 3M* Singlet exciton fission 1 D* processes 1D*-+1M*+1M Dissociation 1D* -+ 1M+ 1M + hVD Fluorescence 1D* --i> 3D* Intersystem crossing 1D*-+1M+1M Dissociative internal conversion 1D* + hV--i>1D** Absorption 1 D** processes 1D** -+ 1M** + 1M Dissociation 1D** -+3D** Intersystem crossing 1D**-+1D* Internal conversion 1D**-+1M+1M Dissociative internal conversion 3 D* p rocesses 3D*-+3M*+1M Dissociation 3D* -+ 1M+1M + hVN Phosphorescence 3D* -+ 1M + 1M Dissociative intersystem crossing 3D* + hv -+ 3D** Absorption 3 D** processes 3D** -+3M **+ 1M } Dissociation 3D** -+ 3M* + 3M* 3D** -+ 3D* Internal conversion 3D** -+ 1M+1M Dissociative intersystem crossing 5 D* processes 5D* -+ 1M*+1M } Dissociative intersystem crossing 5D* --i> 3M* + 1 M 5D* -+3M*+3M* Dissociation 1

1 J

Rate parameter

§7.1 §7.8

kDM

kNT kMTT kNTT

Ref.

1 l

Jk

TT

§8.4ff §6.15 §7.17 §5.14 §6.15 §11.8 §7.1 §7.1 §7.16 §7.16 §5.14 §7.16 §5.14 §7.16 §7.18 §7.18 §7.18 §7.16

§8.8 §8.8

41

Photophysical Processes Table 2.4 Heteropolar bimolecular interactions and exciplex processes (see Chapter 9)

Process

Description

Rate parameter

Interactions 1M + 1Q ->- I(M.Q) Complex formation 3M* + 1Q ~ 3E* Triplet exciplex formation kXT 1M* + 1Q ~ 1E* Singlet exciplex formation kEM 3M* + 3Q* ~ 1.3,sE* Triplet-triplet interaction (Other processes analogous to these in Table 2.3 are also possible. See Chapter 10 for exciplexes with 2NO and 30 2). Complex and exciplex processes I(M.Q) ~ 1M + 1Q Complex dissociation I(M.Q) + hv ~ IE* Charge-transfer absorption IE* ~ 1M* + 1Q} IE* ~ 1M + 1Q* Singlet exciplex dissociation IE* ~ 1M + 1Q + hVE IE* ~ 3E* 3E* ~ 1M + 1Q 1E* ~ 2M+ + 2Q3E* ~ 3M* + 1Q } 3E* ~ 1M + 3Q* 3E* ~ 3E* ~ 3E* ~ sE* ~ SE* ~

1M + 1Q + hvx 1M + 1Q 2M+ + 2Q1M* + 1Q } 1M + IQ*

Fluorescence Intersystem crossing Dissociative internal conversion Dissociation into ions Triplet exciplex dissociation Phosphorescence Dissociative intersystem crossing Dissociation into ions Quintet exciplex dissociation

kME

kQE kFE kXE kGE kCE

kTX kux

k px

kGX k cx

Photophysical Processes

42

Table 2.5 Rate parameter notation kFM,kFD,kFy,kFE,kFH kIM, kID, k ly, kJE kTM' kTH kTD kND kXE kOM' kOD' koy, kOE' k~B, kG}, kON,kGX kPT' k pN , k px kGT kMT kQM[Q], kQD[Q], kQy[Q], kQT[Q] kyM[Y], kYD[Y], kYT[Y] kDMPM] kNTPM] kEMPQ] kXTPQ] kMD kTN kME kQE k TX kux kCE' k cx kMH kDJ kIH' ku kJHPM] kHJ kNJ k MTT [3M*] k DTT [3M*] k GTT [3M*] kTTMPM]

Fluorescence of IM*, ID*, Iy*, IE*, IM** Internal quenching of IM*, ID*, IY*, IE* Intersystem crossing to 3M* from IM*, IM** Intersystem crossing to 3M* (and 1M) from ID* Intersystem crossing to 3D* from ID* Intersystem crossing to 3E* from IE* Internal conversion to ground state from IM*, ID*, Iy*, IE*, IM**, ID**, 3D*, 3E* Phosphorescence of 3M*, 3D*, 3E* Intersystem crossing to 1M from 3M* Intersystem crossing to IM* from 3M* External quenching by [Q] ofIM*, ID*, Iy*, 3M* Energy transfer to [Y] from IM*, ID*, 3M* Formation of ID* from IM* and PM] Formation of 3D* from 3M* and PM] Formation of IE* from IM* and PQ] Formation of 3E* from 3M* and PQ] Dissociation into IM* (and 1M) of ID* Dissociation into 3M* (and 1M) of3D* Dissociation into IM* (and IQ) of IE* Dissociation into IQ* (and 1M) of IE* Dissociation into 3M* (and IQ) of 3E* Dissociation into 3Q* (and IM) of 3E* Dissociation into ions of IE*, 3E* Internal conversion to IM* from IM** Internal conversion to ID* from ID** Internal quenching of IM**, ID** Formation of ID** from IM** and PM] Dissociation into IM** (and 1M) of ID** Intersystem crossing to 3D* from ID** Interaction of 3M* and 3M* to yield IM* (+ 1M) Interaction of 3M* and 3M* to yield ID* Interaction of3M* and 3M* to yield 1M (+3M*) Interaction of IM* and 1M to yield 3M* and 3M*

kM = kFM + kID = kFM + kTM + kGM kD = kFD + kID kE =kFE + kJE kT =kPT + kGT kN =kPN +kON kx = k px + k GX + k TX + kux + k cx kH = kMH + kIH(+k FH ) kJ = kDJ + ku(+kFJ) kTT= kMTT + kDTT + kOTT

2.6 References

43

2.6 References 1. J. B. Birks, The Theory and Practice of Scintillation Counting, Pergamon Press, Oxford, 1964. 2. J. B. Birks, L. G. Christophorou and R. H. Huebner, Nature, 217, 809 (1968). 3. J. B. Birks, D. J. Dyson and I. H. Munro, Proc. Roy. Soc. A, 275, 575 (1963).

3 Absorption 3.1 Vibronic states

The total energy (EI ) of a molecule in its electronic ground state (excluding translational energy, and internal nuclear energy), (3.1) is the sum of three components, the electronic energy (Ee ), the vibrational energy (Ey), and the rotational energy (Er). Similarly, the total energy (ED of a molecule in an excited electronic state (3.2) is the sum of its electronic, vibrational and rotational components, E;, and E/, respectively. If we define an absorption transition as

E~

(3.3) where x = t, e, v or r, then LlEr ~ 10 cm- i , LlEy ~ 1000 cm- i , and LlEe ~ 30,000 cm- i . Transitions involving only LlEr (LlEe = LlEy = 0) yield the rotational absorption spectrum, which occurs in the far infrared region. Transitions involving LlEy and LlEr (LlEe = 0) yield the vibrational and vibrationalrotational absorption spectrum, which occurs in the near infra-red region. Transitions involving LlEe and LlEy (LlEr can be neglected in comparison with LlEe and LlEy) yield the electronic and electronic-vibrational absorption spectrum, which occurs in the visible and ultraviolet region. A state involving electronic and vibrational energy is referred to as a vibronic state, and a transition between two such states is a vibronic transition. Each electronic absorption transition LlEe gives rise to an absorption band system, each band of which corresponds to a different value of LlEy. A molecule as complex as an aromatic hydrocarbon possesses many alternative vibrational modes, but only a few of these, such as the C- C stretching vibrations, are normally dominant in the room-temperature

45

3.1 Vibronic States

electronic absorption spectrum. At low temperatures more detailed vibronic structure is resolved, but at normal temperatures molecular rotation (LlEr), thermal broadening and/or solvent interaction effects (§4.l2) blur the vibronic structure of each electronic band system into a sequence of a few relatively broad maxima. In some compounds with many degrees of freedom, e.g. those with C-C bonds between separate phenyl groups, such as p-terphenyl , the electronic absorption band system may appear structureless.

E~ + t E~v

----1..----

E~ + i E~v

3

2

t

E'e

0 I 0

o

I

~

N

r then (3.4) where m = 0, 1, 2, ... is the vibrational quantum number. If the energy

46

Absorption 3.3

of the fundamental vibrational mode in the excited electronic state is then

E~v,

(3 .5)

where n = 0, I, 2, .. .. If the ground state system is in thermal equilibrium at absolute temperature T, the fraction fm of ground state molecules in a vibrationally excited state m is determined by the Boltzmann factor, (3.6) fm = exp(-mEly/kT) I where k is Boltzmann's constant. Since Ely ~ 1000 cm- , and kT ~ 200 cm- I at room temperature,1I ~ e- 5 = 6·7 x 1O- 3,f2 ~ e- 10 = 4'5 x 10-5 , etc., i.e. over 0·99 of the molecules are in the zero-point vibrational level of energy Et

= Ee + :tE ly

(3.7)

The transitions constituting the main electronic absorption spectrum are given by (3 .8) LIE. = (E; - Ee) + ·t(E~v - Ely) + nE~y (3.9) (E; - Ee) + nE~v since E~y ~ E lv • The lowest energy vibronic transition in a given band system (n = 0) is described as the 0 - 0 transition. The transition to the nth vibrational level of E; is the 0 - n vibronic transition. The main electronic absorption spectrum thus yields data about the vibrational levels (nE~v) of the excited electronic states (Figure 3.1). ~

3.2 Hot bands Weak absorption bands are sometimes observed adjacent to, but at lower energies than, the lowest energy 0 - 0 transition in the main electronic absorption spectrum. These are known as hot bands, and they represent transitions from the vibrationally excited ground state E t (m = I, 2) to E; (n = 0) (Figure 3.1). The hot bands lie at energies of mElV below the 0 - 0 transition, and their intensity decreases with T, according to the Boltzmann factor fm (3.6). The study of hot bands as a function of T has proved useful in the location of the lowest 0 - 0 transition in molecules in which the latter transition is weak or forbidden by symmetry (§1.4) (e.g. benzene, naphthalene). 3.3 The extinction coefficient If a monochromatic beam of light of intensity Ii is incident normally on a specimen of thickness d (em), containing n' molecules of the absorbing species per cm 3 , the intensity I of the emergent beam {3.'10)

3.4 The Born-Oppenheimer Approximation

47

defines the molecular absorption cross-section a (cm2) and the absorption coefficient fL (cm- I ). These parameters are commonly expressed in terms of the decadic molar extinction coefficient €, defined by

1= I j lO-f [M]d

(3.11 )

where [M] is the molar concentration (moles/litre) of the absorbing species. Since n' = N[M] x 10-3 (3.12) where N (= 6·02 x 10 23 ) is Avogadro's number, comparison of (3.10) and (3.11) gives 2303€ a = ~- = 3·81 X 10- 19 € (cm2) (3.13) N

Absorption spectra are preferably plotted in terms of loglo€ against wavenumber v (in cm- I ), but other units are often used . The wavelength '\, which is measured in A or nm (1 A = 10-8 cm, 1 nm = 10-9 m = 10 A) is the reciprocal of the wavenumber v, measured in cm- I or K (= Kaiser) (v = 1 kK = 1000 cm- I is equivalent to ,\ = 10 5 A = 104 nm). v is also expressed in terms of its equivalent photon energy, E = hcv, where h (= 6·63 x 10-27 erg S-I) is Planck's constant, and c (=3·0 x 10 10 cm S-I) is the velocity of light. Alternative energy units include the electron-volt (1 eV = 1·60 x 10- 12 ergs/molecule = 23·06 kcal/mole), which is equivalent to v= 8068 cm- I , and,\ = 1240 nm. 3.4 The Born-Oppenheimer approximation Just as the total energy (Eo E;) of the ground and excited vibronic states has been described as the sum of electronic (Ee, E;) and vibrational (Ey, E~) energies, the wavefunction (tjJ) of a vibronic state can be expressed as the product of electronic (8) and vibrational (ifJ) wavefunctions. This is the Born-Oppenheimer approximation. Thus we may write (3.14) as the wavefunction of the mth vibrational state of a lower electronic state I, and (3.15) as the wavefunction of the nth vibrational state of a higher electronic state u. These wavefunctions form the basis for the quantum-mechanical theory of radiative and radiationless processes in molecules. Initially we consider their application to absorption. I For simplicity it is assumed that each vibronic state is single; if degeneracies occur in either the electronic or

Absorption 3.5

48

vibrational parts of the wavefunction, they can be summed appropriately when necessary. 3.5 The Einstein coefficients Consider a large number of molecules, immersed in a transparent medium of refractive index n, in thermal equilibrium within a cavity at temperature T. The radiation density (erg cm- 3 per unit frequency range) of frequency v within the medium is given by Planck's black-body radiation law 87Thv 3 n 3 /c3 p(v) = {exp(hvlkT) _ I}

(3.16)

The rate of molecules going from state 1m to state un by absorption of radiation is (3.17) where N 1m is the number of molecules in state 1m, Vlm -> un is the frequency of the transition, and B,m->un is the transition probability coefficient, known as the Einstein B coefficient. Molecules in state un can go to state 1m by spontaneous emission with transition probability Aun->'m (the Einstein A coefficient), or by induced emission with probability Bun->lmP(Vun->lm). The rate at which molecules undergo this downward transition is given by (3.18) where (3.19) (3.20) and Nun is the number of molecules in state un. At equilibrium the rates of the absorption and emission transitions are equal, so that by equating (3.17) and (3.18), Aun ->Im =

B

un ~ lm

(N,m _ N un

1) P( ) Vun->Im

(3.21)

The number of molecules in the two states at equilibrium are related by the Boltzmann distribution law

un N = exp [-hvun->'m/kT] (3 .22) N 1m Substitution of (3.16) and (3.22) in (3.21) gives the Einstein relation between the A and B coefficients for molecules in a medium of refractive index n, (3.23) The Einstein A coefficient determines the probability of spontaneous emission, i.e. luminescence, and its relation to the fluorescence spectrum

49

3.5 The Einstein Coefficients

and lifetime will be discussed in Chapter 4. The Einstein B coefficient determines the probability of absorption, and it is simply related to the molecular absorption cross-section a. By the definition of a (3.10), the change in radiation density dp(v) of a beam of radiation density p(v) in assing through a thin layer dx of a specimen containing n' absorbing P 3 . molecules per cm IS dp(v) = -an' p(v) dx -aNIOP(v)

=

(3.24)

where NIO is the number of absorbing molecules per cm 2 in the ground state 10. The number of molecules per cm 2 excited per second with energy hI' is LlN(v) = -c dp(v)Jhvn (3.25) so that combining (3.24) and (3.25) LlN(v)

=

NIO cap(v) hvn

(3.26)

Integrating over the (10 -i> un) vibronic band, we obtain the absorption probability for this transition as C

LlNlO-->un = NIO [ hn

Comparison with (3.17) gives B

lO-->un -

C

hn

f

-

f

- v-

a(v)dv]

P(VIO-->un)

a(v)dv

_ 2303c

- hnN

1' -

f

e(v) dv -

1'-

(3 .27)

(3.28) (3.29)

from (3.13). If we assume that all the molecules originate in the 10 state, summation of (3.29) over all the vibrational levels of the upper electronic state gives the probability of all transitions to the u state: (3.30)

=~ hn

f

a(v)dv

_ 2303c

- hnN

f

v

e(v) dv - v-

(3.31 ) (3.32)

where the integrals are now over the whole I -i> U electronic absorption band system.

Absorption 3.6

50 3.6 Transition moments

Using the Born-Oppenheimer approximation (§3.4) we may write

ifJlO(X, Q) = Bj(x, Q) 4\o(Q)

(3.33)

ifJun(x, Q) = Bu(x, Q) ifJu, is defined by the integral (3.35) where r i is the position vector of the ith particle (electron or nucleus) of charge Zi e in the molecule. For the 10 -+ un vibronic absorption transition, we obtain MIO->un=e

JJifJio(x,Q){tri-~zllrll}ifJun(X,Q)dXdQ

(3 .36)

where suffixes i and JL refer to the electrons and nuclei, respectively. Substituting from (3.33) and (3.34), and separating the electronic and nuclear coordinates, MIO->un = e

Jlm(Q)dQ

= uoIMullcJ>lm) Hence

AuO->lm oc

I F(v) dv

(4.4) (4.5)

where the integral is taken over the uO -+ 1m vibronic fluorescence band. 4.2 The mirror symmetry relation We may compare (4.4) with the corresponding equation for the 10 -+ un vibronic absorption transition MIO->un =

I cJ>{o(Q) M1u(Q) cJ>un(Q) dQ

(3.39)

If the nuclear configurations of the ground (I) and excited (u) electronic states are sufficiently similar that the vibrational wavefunctions are the same in I and u, i.e. cJ>1O = cJ>uo, cJ>lm = cJ>um, M 1u = Muh then from (3.39), (4.4) and (4.3), (4.6) MuO->lm = MIO->um (4.7) BuO->lm = BIO->um Relation (4.7), which should not be confused with the Einstein relation, Bun->Im = B1m->un

(3.19)

Fluorescence 4.2

86

provides the theoretical basis for the empirical mirror symmetry relation between the fluorescence and absorption spectra, which is commonly observed. For the fluorescence spectrum, from (4.2) and (4.5), BuO--,> lm ex:

1 -:3 nr

J

F(v)dv

(4.8)

- -3-

v

where nr is the mean refractive index of the solvent over the fluorescence band . For the absorption spectrum, from (3.29), (4.9) where na is the mean refractive index of the solvent over the absorption band. The mirror-symmetry relation (4.7) can be tested experimentally by (b)

(0)

~

15

1'01 "0

t

0·3

~ 0

~

E u

"0

'">

0 ·2 11 .c '" .g'"

10

~

" ·5 ~O

0·1

s; ~ ~,

0 26

24

30

28

26

24

22

~

is ~,

ui~

> '" ~ ;::; u,,~_

:

04

2

~

"

"to? I

~

u..

"-

0 2

"

u.:.

0

0 j;

(10' cm- 1 )

Figure 4.2 Mirror symmetry relation. Modified absorption spectrum E(ii)/ii (left-hand solid curve, ordinates as shown); and modified fluorescence spectrum F(ii) /ii 3 (right-hand solid curve, ordinates normalized) and its reflex ion F(2iio - ii)/(2ii o - ii)3 (left-hand broken curve) about mean wavenumber iio (arrow). Benzene solutions of (a) perylene, (b) anthracene, (c) 9,IO-diphenylanthracene, (d) PO POP (after Birks and Dysonl) a comparison of the modified absorption spectrum, E(V)/V, and the reflection, F(2v - vo)/(2v - vO)3, of the modified fluorescence spectrum, F(v)/v\ about the 'mirror-symmetry' frequency Vo. Figure 4.2 shows such a comparison for four compounds. I The mirror symmetry relation is generally found to

4.3 The Radiative Lifetime

87

be approximately valid for the condensed aromatic hydrocarbons. Deviations from it indicate differences in the nuclear configurations in So and SI '

4.3 The radiative lifetime The radiative lifetime TFM is defined as the reciprocal of the radiative transition-probability kFM (in S-I). kFM is equal to the Einstein A coefficient summed over the complete fluorescence spectrum,I-2 i.e.

2m AuO-->lm

A uo ... 1 =

I/TFM = kFM =

(4.10)

Substituting from (4.2), (4.3) and (4.4) 3 kFM = 87Thnt c- 2 V~o-->Im B uO ... 1m

(4.11)

m

= 87Thntc- 3 KI M u.\2 ~ V~o-->Imlf :o(Q) lm(Q)dQI

2

(4.12)

where MUI is the mean value of Mul(Q) [cf. equation (3.40)]. Since the lmCQ) wavefunctions form a complete orthonormal set (4.13) Hence the sum in (4.12) can be equated to

2

~ V~o"'lmlf :o lm dQI

21f:o lm dQr

f F(v) dv

=

f F(v~ v

m

(4.14) dv

Each term in the numerator of (4.14) is proportional to the intensity of one vibronic band in the fluorescence spectrum, and each corresponding term in the denominator is proportional to v- 3 times the intensity of the vibronic band. We write -3 _I _

0) is now

(4.25) so that (4.26) (4.27) where (4.28) is defined as the molecular fluorescence lifetime. Integrating the total fluorescence quantum intensity, we obtain co

qFM =

f iM(t)dt = kFM/kM o

(4.29)

in agreement with (4.24). We thus obtain the following relations between the basic fluorescence parameters: (4.30)

90

Fluorescence 4.5

4.5 Competing bimolecular processes There are four bimolecular processes which commonly compete with fluorescence emission (and internal quenching) in solutions, and thereby modify the fluorescence characteristics. (i) Collisional impurity quenching. If the solution contains a molar concentration [Q] of an impurity molecule Q, diffusion-controlled collisions between IM* and Q may lead to impurity quenching of the IM* excitation. If the rate parameter of impurity quenching is kQM (M- 1 S-I), then a further term (-kQM[Q] [lM*]) is added to the rate equations (4.23) and (4.25). Due to the presence of [Q], the fluorescence quantum yield is reduced from qFM (4.24) to (4.31) and the fluorescence lifetime is reduced from its molecular value TM (4.28) to (4.32) The ratio is (4.33) as in the absence of [Q]. The mechanism of impurity quenching is discussed in §9.9. Oxygen, which is present at [Q] ~ 2 x 10- 3 M in aliphatic solvents in equilibrium with the atmosphere, is the commonest and most effective impurity quencher, in that every molecular encounter with O 2 results in the quenching of 1M*. The oxygen quenching can be reduced either by bubbling oxygen-free (white spot) nitrogen through the solution, thereby replacing the dissolved oxygen by nitrogen which is not an impurity quencher, or most effectively by cyclic freezing and pumping of the solution to remove all dissolved gases. The presence of dissolved oxygen in a hexane solution of benzene reduces the benzene fluorescence lifetime from TM = 26 ns to T = 5·7 ns, and the fluorescence quantum yield is reduced by a similar factor of 4·5. In compounds with larger TM the oxygen quenching of the fluorescence is even more pronounced. The mechanism of oxygen quenching is discussed in §1O.4. (ii) Energy transfer quenching. If the solution contains a molar concentration [Y] of an aromatic impurity Y, whose first electronic excited singlet state SlY lies below that of IM*, a further type of IM* impurity quenching can occur, due to non-collisional radiationless energy transfer to Y. In low-viscosity solutions and in some other systems, e.g. aromatic crystals,

91

4.5 Competing Bimolecular Processes

the IM* quenching can be described by a constant rate parameter k yM , in a similar manner to collisional quenching, so that a further term (-kyM[Y] PM*]) is added to the rate equations (4.23) and (4.25), giving (4.34)

T =

1

kFM

+ kIM + kyM[Y]

TM

= -:----7---:=

1 + TMkyM[Y]

(4.35)

and a relation analogous to (4.33). In high-viscosity solutions k YM is a function of time t, and the IM* fluorescence decay becomes non-exponential. This behaviour is discussed in §11.10. The presence of the two types of impurity quenching emphasises the necessity for extreme purity of all solvents and solutes used in fluorescence studies. Solvents should be of spectroscopic purity and of fluorometric grade, i.e. no fluorescence should be detectable from the pure solvent, unless it is an aromatic compound. Solutes should be of the highest commercial purity, and they should be SUbjected to the standard chemical purification techniques, e.g. fractional distillation, recrystallization, and/or column chromatography. Zone-refining and microsublimation are the most suitable methods for the further purification of aromatic compounds. These purification techniques should be undertaken in an inert atmosphere, in the absence of oxygen, since the aromatic hydrocarbons are prone to oxidation, apart from the quenching effect of molecular oxygen. Some compounds, such as anthracene and the higher polyacenes, are photochemically active, particularly in solution, and such materials should be stored in dark containers. The maximization of the fluorescence lifetime T or of the fluorescence quantum yield CPFM often provides a sensitive and suitable criterion of purity.6 The presence of any fluorescent impurities with Sl below that of the principal compound can be detected by the occurrence of longer wavelength bands in the fluorescence spectrum. (iii) Concentration quenching. The increase of the molar concentration PM] of the fluorescence solute commonly causes a decrease in the molecular fluorescence quantum yield CPFM' This concentration quenching or self quenching of the IM* fluorescence is due to excimer formation (§2.4), which will be discussed more fully in Chapter 7. Since this is a diffusion-controlled collision process, it can be described in first approximation by a rate parameter kDM resulting in a further term, (-kDMPM] [iM*]), being added to the rate equations (4.23) and (4.25), giving tP

'" FM - kFM

kFM

_

+ k nd + kDMPM] -

qFM 1 + TMkoMPM]

(4.36)

Fluorescence 4.5

92

I

T

TM

~ kFM + kiM + kOM[lM] = I + TMkoM[lM]

(4.37)

leading to (4.33). Equations (4.36) and (4.37) are only approximate: the exact expressions are derived in Chapter 7. (iv) Radiative migration. There is commonly an overlap of the 0 - 0 bands of the fluorescence and absorption spectra. When the latter is a p-band, i.e. SI = lL., as in anthracene or perylene, the spectral overlap may be considerable and lead to self-absorption of part of the fluorescence emission, except in very dilute and/or very thin solutions. This corresponds to radiative migration of the IM* excitation. It competes with the escape of the fluorescence from the specimen and it changes the observed (technical) fluorescence lifetime and quantum yield from their true (molecular) values. Consider a fluorescent system with fluorescence quantum efficiency qFM and lifetime TM, in which a is the probability of self-absorption of an emitted photon, so that (l - a) is the photon escape probability. Photons which are absorbed are re-emitted with quantum efficiency qFM and lifetime TM' The technical quantum yield cJ>FM of the escape of the fluorescence is given by,7 cJ>FM = qFM(1 - a) [1 + aqFM + a2q~M + ... ] qFM(i- a) 1- aqFM

(4.38)

The successive terms in the series correspond to photon escape after 1, 2, 3, ... emissions. Self-absorption decreases the rate of decrease of [IM*] from (4.25) to d[l:*] = -{(I - a)kFM + kiM} [lM*]

= -[IM*]/T

(4.39) (4.40)

since the excitation of akFM[IM*]dt molecules does not escape. The technical fluorescence lifetime is increased to T

1 (l - a)kFM

= -;-:----:-::-----:--

+ kiM

(4.41) (4.42)

The self-absorption parameter a depends on the overlap of the absorption spectrum E(ii) and the fluorescence spectrum F(ii), on [1M], and on the

4.5 Competing Bimolecular Processes

93

specimen thickness x through which the fluorescence photons have to escape. In terms of these parameters

f F(ii){l

c:

'cr" ::l

'"

.2:

10

from (4.21), are listed in Table 4.2. For most of the compounds (TFM)t .;;; TFM, in agreement with the previous conclusions. The use of(4.21), rather than the more exact relation (4.19), is reasonably justified since many

102

Fluorescence 4.8

of the meso-substituted anthracenes exhibit approximate mirror symmetry between their absorption and fluorescence spectra. Berlman4 has observed TM and q F M for more than seventy aromatic compounds in dilute deoxygenated cyclohexane solutions. The compounds include several of interest as organic scintillator solvents and solutes. He compared the experimental values of TFM with the theoretical values of (TFM)t derived from equation (4.21), which is based on the mirror-symmetry relation. The results, which are summarized in Table 4.3, show reasonable agreement between TFM and (TFM)t except for a few compounds, such as 1,6-diphenylhexatriene, which have been discussed above, and the biphenyl derivatives, to be considered in §4.9. In a subsequent empirical analysis of these data based on the approximate 'atomic' relation (4.22), Berlman2 6 replaced the absorption integral f E(ii)dii by LliiEmm where Em•x is the maximum value of E(ii) in the first absorption band system, and Llii is the half-width, which he assumed to be constant for all the molecules. A double-logarithmic plot of TFM (in a common solvent, cyclohexane) against Em • x • ii~1 showed the expected approximate inverse proportionality between these two quantities over nearly three decades, although there is a degree of scatter du~ to the simplifying assumptions made in the analysis. Seybold et al. 35 have determined the fluorescence and absorption spectra, the fluorescence lifetime TM , and the fluorescence quantum yield cP FM of fluorescein and nine of its brominated derivatives in basic ethanol solutions. They used both a standard photometric technique (§4.7) and a calorimetric technique for the determination of cPFM • The latter is based on the fact that in the absence of photochemical reactions the absorbed photon energy is either emitted as luminescence (as fluorescence in room temperature solu" tions, where the phosphorescence yield is negligible) or dissipated as heat. They compared the rate of heating of the fluorescent dye solution with that of a similar non-fluorescent dye solution (aniline blue black) under similar conditions of steady irradiation. The heating of the solution was observed by its thermal expansion up a capillary tube attached to the specimen cell. TM was determined using a pulse fluorometer, the observed data being corrected forthe instrumental response using the convolution integral (4.51). The results are listed in Table 4.4. (cPFM)c. 1 and (cPFM)Ph are the values of cP FM determined calorimetrically and photometrically, respectively, TM is the observed fluorescence lifetime, and (TFM)c.1 (= TM!(cPFM)cal) and (TFM)Ph (= TM!(cPFM)Ph) are the corresponding radiative lifetimes. The latter are compared with the theoretical values (TFM)t obtained from the spectra and the Strickler-Berg relation (4.20), the mirror-symmetry relation (4.21), and the atomic resonance relation (4.22), respectively. Taking the mean values for (TFM)cal and (TFM)t for nine compounds, (TFM)cal is 0·2 ns less than

4.9 Fluorescence Lifetimes and Quantum Efficiencies

103

(TFM)' from (4'20), it agrees closely with (TFM)' from (4.21), and it is 0·6 ns greater than (TFM)' from (4.22), demonstrating the superiority of the first

two relations, which agree with the data within the range of probable error. 4.9 Fluorescence lifetimes and quantum efficiencies

The experimental values of TM, qFM and TFM for aromatic compounds in dilute deoxygenated solutions at room temperature are listed in Table 4.5. Similar data for other aromatic compounds are given in Tables 4.1-4.4 and in the review by Birks and Munro. 9 In the absence of pronounced solvent-solute interaction, the absorption and fluorescence spectra of an aromatic compound are reasonably independent of the nature of the solvent, apart from slight solvent spectral shifts and changes in vibrational resolution (§4.12). Hence, from (4.20), we can write (4.55) where n is the mean refractive index of the solvent, and (TFM)O and (kFM)O are the values of TFM and kFM' respectively, referred to a medium of refractive index n = 1. Equation (4.55) provides a method of comparing the values of TFM obtained for a given molecule in different solvents, since (TFM)O should be independent of the solvent. Such comparisons, using the data of Table 4.5, indicate that (4.55) is probablY valid within the experimental error, though more accurate data obtained on the same compound in a wide range of solvents of different n are desirable to provide a more stringent test of (4.55). The experimental values of qFM are subject to larger uncertainties than those of TM' Berlman,4 who obtained the data of Table 4.3, evaluated qFM by comparison with a cyclohexane solution of 9,1O-diphenylanthracene (DPA) for which he assumed a value of qFM = 1'0, based partly on the ethanol solution data of Bowen and Sahu (Table 4.5, ref. y). This normalization is considered to be in error for the following reasons. (i) Other observers (Table 4.5, refs. i, p, q, t, u, v, z, S) have obtained values of qFM < 0·89 for DPA in various solvents, with a mean value of qFM = 0'83. (ii) Similar values of qFM were observed 1,23 for DPA in benzene, and these give values of TFM in close agreement with the values obtained from the theoretical relation (4.19) (Table 4.1). (iii) Horrocks et al. (Table 4.5, ref. z) observed a triplet quantum yield kPT' the competing radiative (phosphorescence) rate; and there are reliable experimental data available on most of the aromatic hydrocarbons of interest.

5.6 The Theory of Radiationless Transitions

149

Table 5.3 gives a comprehensive list of the experimental values of the T, - So (0 - 0 transition) energy ET and the triplet lifetime TT of the unsubstituted aromatic hydrocarbons and their perdeuterated derivatives. This is an extension of the list originally compiled by Siebrand. 7 The data are mainly for solutions in EPA (ether/isopentane/alcohol) glass at 77°K. The parameter "I is the relative number of hydrogen atoms in the hydrocarbon, C'-'lH'l' In all cases deuteration of the hydrocarbon increases TT. Observations of qPT and TT for typical hydrocarbons indicate that the phosphorescence rate k pT ::::: 0·03 s-' (§6.6). The values of the T, - So intersystem crossing rate kGT' listed in Table 5.3, are evaluated 7 on the assumption that kPT = 0·03 S-1 for all the compounds. Figure 5.1 plots the T, - So intersystem crossing rate kGT (S-I) against the energy gap ET (em-I). The following features are of interest. (i) kGT is always reduced by deuteration of the compound. (ii) There is a broad correlation between kGT and En in that kGT increases with decrease in ET • (iii) All compounds with the structural formula C 1s H 12 ("I = 0·40), lie on a linear plot of 10gkGT against ET. (iv) Compounds with "I > 0·4 tend to lie above this line, and those with "I < 0·4 tend to lie below it. These features lead to the empirical linear relations 7 - s between 10gkGT and (ET - Eo)/n plotted in Figure 5.2, where Eo = 4000 cm- 1 for protonated compounds, and Eo = 5500 cm- 1 for deuterated compounds. These relations are explained by the theory described in §§5.7-5.9. 5.6 The theory of radiationIess transitions The theory of radiative transitions was considered in Chapters 3 and 4. To summarize, the probability k~u of a radiative transition from an initial vibronic state of wave function fuo (= Ou c.P uo , where Bu, c.P uo are the electronic and vibrational wavefunctions, respectively) to a final vibronic state of wavefunction f'm (= 01c.P 1m), is proportional to the square of the electric dipole transition moment, k~u cc IMuo->lml2 = =

=

l12

I12 2 IM1u121 S uo, 'm1

(5.11)

where M' is the electric dipole operator. The Born-Oppenheimer approximation (§3.4) permits separation of the electronic (0) and vibrational (c.P) wavefunctions, so that k~u is proportional to the product of the electronic

150

Radiationless Transitions 5.6

transition moment iM: 1u i2 and the vibrational Franck-Condon factor iSuO.lmi2, which is the square of the vibrational overlap integral (3.41). The radiative transition probability for the vibronic transition is given by (5 .12)

where A 1u is the Einstein A coefficient for the complete electronic transition, and the Franck-Condon factor F= iSuO.lmi2. Various approaches have been made to the theory of radiationless transitions. Gouterman9 treated radiationless transitions in a similar manner to radiative transitions, except that the photon field was replaced by a phonon field. He assumed that radiationless transitions do not occur in the absence of a solvent environment, a hypothesis which is inconsistent with the observation of internal conversion and intersystem crossing processes in vapours at low pressures (§§4.12, 6.16). Robinson and Frosch,IO-11 Hunt, McCoy and Rossl 2 and Siebrand 7 - s . 13 have taken the opposite point of view. They have treated the case where the radiationless transition rate is determined by intramolecular interactions, the role of the medium being restricted to that of a source or sink of thermal energy. Hunt et alP calculated potential-energy surfaces for the electronic states, and derived the rate of radiationless transitions between two states empirically from the distance between the corresponding potential-energy surfaces. The approach of Robinson and Frosch 1o - 11 is based on vibrational overlap or Franck-Condon factors, and it stresses the formal analogy to the theory of radiative transitions, summarized by (5.11) and (5.12). They did not attempt a direct calculation of F, but sought an empirical relation between F and the energy gap between the initial and final electronic states. Siebrand 7 - 8 • 13 has developed a quantitative theory of radiationless transitions in low-temperature solutions, and it is his treatment which is described in more detail below. Robinson,14 Bixon and Jortner l5 and Chock et al. 51 have recently discussed intramolecular radiationless transitions in isolated molecules. We consider a molecule interacting with a solvent at low temperatures; The electronic states of the system (for fixed nuclei) are el and u with energies EI < Em and with corresponding vibrational states ifJ1(E) and ifJu(E), where E is the vibrational energy measured relative to the zero-point energies EI and Em respectively. Initially the system is in the state uifJu(O), which is an exact eigenstate in the Born-Oppenheimer approximation. If we go beyond this approximation there is a non-zero matrix element of the form

e

e

(5.13)

5.6 The Theory of Radiationless Transitions

151

where I N is the nuclear kinetic energy operator. Hill is negligible, except when E::: Ell - E I • Its main effect is that it induces radiationless transitions from Oll to 01, If the solvent causes rapid vibrational relaxation in 01 (§5.1), the transition is irreversible and it can be described by time-dependent perturbation theory. In polyatomic molecules, where one has a large number of states 01 @I(E) and these are broadened by solvent interactions, they merge into a continuum of state density PE' The radiationless transition probability per unit time is then given by lO- 1I 2 Rr = 477 PE IH 12 k III (5.14) h2 III Hill can be separated into electronic and vibrational components in a manner similar to MuO->lm (5.11), by writing H lu = and suffix i refers to the osciIIator which includes the heavier isotope. For an isotopicaIly-substituted compound (5.29) thus yields (5.35) where zj(al/ 2 x; av) :::: z(x;v), if z is a slowly varying function of v. This gives the foIIowing isotope rule F{(E ) = aF'(E)

(5.36)

The same rule can be derived from (5.21)-(5.23), (5.25) and (5.31) for the other types of osciIIator, provided v is not too small. In comparing two molecules or two classes of molecules which differ only by isotopic substitution, the logarithmic derivatives of the Franck-Condon factors are proportional to the vibrational frequencies of the modes which are mainly responsible for the radiationless transition. This provides a means of identification of these modes.

5.9 T I

-

So intersystem crossing: comparison of theory with experiment

The experimental data of 10gkGT against ET plotted in Figure 5.1 show that these quantities are correlated, though the correlation is not direct. The degree of correlation is greatly improved by dividing ET by TJ, the relative number of hydrogen atoms in the molecule, to take account of structural differences. Plots of 10gkGT against ET/TJ yield good linear fits for both the protonated and deuterated compounds. Equation (5.30) suggests the generalization of the latter quantity to (ET - Eo)JTJ, where Eo represents the crossing-point, introduced in §5.7. The best correlations are obtaining taking E~ = 4000 cm- i and Eg = 5500 cm- I for the protonated and deuterated hydrocarbons, respectively. Figure 5.2 plots 10gkGT against (ET - Eo)/TJ in this manner. The isotope rule (5.36) can be applied directly to the data of Figure 5.2, since the gradients of the plots for the deuterated and protonated hydrocarbons are equal to F;(E) and F'(E), respectively. The experimental value of a = 1'33 thus obtained agrees closely with the value of (!1-CD/!1-CH)i 12 = 1'36, where !1-CD and !1-CH are the reduced masses of CD and CR. This indicates that vibrations of these oscillators take up most of the energy at E> Eo. To a good approximation F(E) for E > E~ can be described solely in terms of CR modes. The same conclusion is also drawn from the appearance of the factor TJ in the correlation function. The behaviour of F(E) for E < Eo is obtained from the phosphorescence spectrum. An analysis of the latter l7 shows that for several hydrocarbons

5.9 T 1 - So Intersystem Crossing: Comparison of Theory with Experiment

157

F(E) is reasonably represented by equation (5.21) for a displaced oscillator, with hWI ~ 1400 cm- I and y ~ 1·5. F(E) at E < Eo is mainly due to totally symmetric CC-stretching vibrations, and it is observed to be insensitive to deuterium substitution. At Eo, where the two parts of F(E) join, they must have a common value of F'(E). This is achieved in Figure 5.2 by drawing the empirical F(E) curves for E > Eo as tangents to the curve for E < Eo, which is obtained from the phosphorescence spectra. The connection between the radiative and radiationless parts of F(E) calibrates the latter. A linear extrapolation of F(E) for E> Eo yields peGT = 4 x 10 4 S-I, in (5.18). Siebrand 7 - 8 concludes that F(E) at E> Eo is dominated by anharmonic distortions of CH- (or CD-) stretching modes, and he obtains a semiempirical equation for F(E), based on the general relation (5.31). All CH-stretching modes are considered quasi-degenerate, so that the degeneracy N is equated to N H , the number of H atoms in the molecule. The expression zlWN in (5.31) is replaced by AvlNe from (5.32), where Ne is the number of C atoms in the molecule. The following relation is thus obtained, for E ;;;. Eo, F(E) = F(E )(A IN. )v(NH+ v - I)! o v e (NH -1)!v!

(5.37)

where E-Eo hWI

V= - -

(5.30)

For protonated and deuterated hydrocarbons Eo = 4000 cm- I and 5500 em- I, respectively, and hWI = 3000 cm- I and 2250 em-I, respectively, corresponding to the CH- and CD-stretching vibrational modes. The only empirical parameters in (5.37) are F(Eo) and A. Siebrand has used two alternative methods to evaluate these parameters. (i) Since kGT is proportional to F from (5.18), equation (5.37) can be written in the form

_ v(NH + v-l)! kGT - kGT(Eo)(AvINd (NH - I)! v!

(5.38)

where kGT(Eo) is the hypothetical value of kGTat E = Eo. A comparison7 of the experimental data on kGT (Table 5.3) with (5.38) gives a reasonable fit for k GT(Eo)=3'5 x 10 5 s-I, A=0·051. Siebrand l6 obtained a similar value of A = 0·0507 from an analysis of the CH-stretch overtone spectrum of benzene, and he equates A to an anharmonicity constant. It should be noted, however, that (5.37) and (5.38) will have a similar form for harmonic CH-stretching vibrational modes. Siebrand and Williams l8 have analysed

158

Radiationless Transitions 5.9

the Franck-Condon envelopes of the fluorescence spectra of anthracene in terms of (5.37), and obtained-the following values: anthracene·h lO (solution), ,\ = 0·08 anthracene·d lo (solution), ,\ = 0·13 anthracene·h lO (crystal), ,\ = 0·039 anthracene·d lO (crystal), ,\ = 0·074 (ii) Siebrand's second method 8 of normalization of the experimental data is that shown in Figure 5.2. As described above, the empirical F(E) curves for E > Eo are drawn tangentially to the F(E) curve at E < Eo, derived from the phosphorescence spectra. This procedure yields values of PCGT = 4 X 10 4 S-I, kGT(Eo) = 10 4 S- I and ,\ ~ 0·1. Although the numerical values of kGT(Eo) obtained by the two methods differ, both procedures give reasonable fits to the experimental kGT data because of the relatively large energy gaps involved in the extrapolation. Method (i) is based on the semi-empirical relation (5.37), which was derived to explain the observed dependence of kGT on (E - Eo)/YJ and isotopic substitution (Figure 5.2) in terms of anharmonic CH vibrations. Siebrand and Williams l8 have subsequently shown that the isotope rule for anharmonic oscillators differs from that for harmonic oscillators, and that the theory predicts a value of a = 1·5 for anharmonic CH oscillators compared with the experimental value of a = 1·33. This indicates that either (a) anharmonicity is unimportant, or (b) modes other than CC- or CH-stretching vibrations contribute substantially to F(E). If hypothesis (b) is valid, as proposed by Siebrand and Williams, 18 it appears inconsistent to describe F(E) in terms of the relation (5.37) derived specifically for CH vibrational modes. The alternative hypothesis (a) removes the discrepancy since, if anharmonicity is unimportant, the experimental value of a = 1·33 indicates that harmonic CH vibrations are dominant at E > Eo, and their contribution to F(E) will be given by a relation similar to (5.37). However, there is other evidence for anharmonicity7 and until the apparent anomaly is resolved the graphical method (ii) appears preferable, since it does not involve any assumptions about the vibrational modes responsible for the radiationless transition. Figure 5.2, which is directly derived from the experimental data, plots the Franck-Condon factor F as a function of

5.10 Energy Gaps

159

(E - Eo)/T). Unlike (5.37), it has the further advantage that it is not restricted to E > Eo. 5.10 Energy gaps The success of Siebrand's analysis of T I - So intersystem crossing in the aromatic hydrocarbons is due to several factors. (i) The energy gap is sufficiently large that the interacting vibrational states form a quasi-continuum. (ii) The Franck-Condon factor F is determined solely by the magnitude of the energy gap and by the vibrational modes of the ground-state molecule. (iii) Reliable values of the energy gap are available. (iv) Reliable experimental values of the radiationless transition probability are available for a large number of protonated and deuterated aromatic hydrocarbons (Table 5.3).

The other types of radiationless transitions do not satisfy all these criteria, but it is clear that the energy gap between the interacting electronic states is an important parameter since it determines the Franck-Condon factor F. Table 5.4 lists the energies of the ILb and ILa states, obtained from the solution absorption spectra (Table 3.1), and of the 3La (T 1) states, obtained from the phosphorescence spectra (Table 5.3 and associated references), for the unsubstituted aromatic hydrocarbons. The small solvent shifts in the energies due to the use of different solvents are negligible in comparison with the magnitudes of the energy gaps. The energy gaps relevant to the various radiationless transitions are as follows:

(a) TI - So intersystem crossing: ET = 3La· (b) SI - So internal conversion: Es = 1Lb or ILa, whichever is the lower. (c) S2 - SI internal conversion: Llss = liLa - lLbl. (d) SI - TI intersystem crossing: LIST = Lb - 3La) or La - 3La), whichever is the lower.

e

e

The values of these energy gaps for the aromatic hydrocarbons are listed in Table 5.4. The analysis ofT 1 - So intersystem crossing may be extended and applied to the other processes in order to predict the radiationless transition probabilities, although there are few relia~le experimental values yet available for comparison. SI - So and S2 - SI internal conversion are treated in this manner in §§5.11 and 5.12, respectively. SI - Tl intersystem crossing is a more difficult process to analyse, since it commonly occurs in parallel

Radiationless Transitions 5.11

160

with SI - Tq intersystem crossing (§5.4), a process which does not satisfy the basic criteria (i)- (iv) of the Siebrand analysis. The discussion ofS I - TI and SI - Tq intersystem crossing will therefore be postponed until after a fuller consideration of ~he triplet state (§6.13). 5.11 SI - So internal conversion

The SI - So energy gap, E s, is greater than the TI - So energy gap, E T , so that the Franck-Condon factor Ffor an SI - So radiationless transition can be estimated by a direct extrapolation of the curves of F against (ET - Eo)frJ (Figure 5.2), substituting Es for ET. The values of F thus obtained for protonated and deuterated aromatic hydrocarbons are listed in Table 5.5. From (5.17) we may write for the SI - So internal conversion rate (5.39) where CGM is the electronic factor for the radiationless transition. In discussing T 1 - So intersystem crossing (§5.9) the factor PCGT = 4 x 104 S- I was obtained by normalization to the experimental values of k GT • Experimental values of kGM are sparse and less reliable than those of kGT (§6.3), and an alternative procedure is therefore adopted to estimate CGM • If we assume that the electronic factors, CGM and CPT, for the radiationless transitions are proportional to the electronic factors, AFM and APT, for the corresponding radiative transitions, then CGM CGT

A FM kFM APT kPT

(5.40

Table 5.6 lists the experimental values of kFM (from Table 5.1) andk PT (from Table 6.2) for several aromatic hydrocarbons. The ratio (kFM /kPT) ~ lOB for all the compounds, so that if P (= 477 2 PE/h) has the same value for the two radiationless transitions, then from (5.39) (5.4l) The values of kGM obtained from (5 .39), (5.41) and Figure 5.2 are listed in Table 5.5. They are compared with the experimental values of kGM' obtained from the fluorescence and triplet quantum yields, in §6.3. Siebrand and Williams lB have independently evaluated kGM for several aromatic hydrocarbons, using a relation similar to (5.38), v(NH + v - I)! kGM=kGM(Eo)(Av/Nc) (NH-l)!v!

(5.42)

with A = 0·051. They chose a value of kGM(Eo) = 3 x 1013 S-I to optimize agreement with the limited experimental data on k GM . Their value of

5.12 S2 - SI Internal Conversion kGM(Eo)/kGT(Eo) ~ 10

161

8

, although based on different criteria, agrees with that of CGM/CGT = 10 8 , obtained from (5.40). Their values of kGM from (5.42), which are listed in Table 5.5, agree closely with the previous values, except for the lighter molecules, benzene, naphthalene and azulene. These molecules have relatively large values of 1), leading to significant differences between the values of F obtained from Figure 5.2 and (5.42).

5.12 S2 - SI internal conversion

A similar procedure may be used to estimate the S2 - SI internal conversion rate kMH' by the following assumptions: (5.43)

(a) kMH =PCMHF

(b) F is given by Figure 5.2, substituting Llss for ET , and (c) PCMH = PCGM = 4

X

10 12 S-I.

The values of kMH thus obtained are listed in Table 5.7. These assumptions require critical appraisal. It is known that radiationless transitions are subject to the same multiplicity selection rules as the corresponding radiative transitions. The electronic factors k pT and CGT for the TI - So CLa - 1A) radiative and radiationless transitions, respectively, each arise from spin-orbit coupling to higher excited states (§6.12). The Siebrand analysis considers k pT and CGT to be constant for the unsubstituted aromatic hydrocarbons, and this is consistent with experiment. The electronic factor kFM for the lLb - IA transition, which is spin-allowed but symmetryforbidden, arises from vibronic coupling to higher excited states, and it is approximately constant for un substituted aromatic hydrocarbons in which SI = lL b . Equation (5.40) assumes that the electronic factor for a radiationless transition is proportional to that for the corresponding radiative transition, so that CGM for SI - So internal conversion is taken to be approximately constant for the unsubstituted aromatic hydrocarbons. The experimental data are consistent with this hypothesis (§6.3). Equation (5.40) implies that radiationless transitions are subject to the same symmetry and parity selection rules as the corresponding radiative transitions. The S2 - SI radiative transition is forbidden, since the two states have a common (u) parity, and no S2 - SI fluorescence has been observed. (Such fluorescence would occur in the infrared region, which has not been extensively explored foremission from the aromatic hydrocarbons.) On the other hand, the experimental evidence for Vavilov's law and Kasha's rule shows that in most compounds the Sz - SI radiationless transition is allowed. There is a simple explanation for the apparent anomaly. Internal conversion occurs from S2 into isoenergetic higher vibronic levels of S(,

162

Radiationless Transitions 5.13

which may differ in symmetry and p arity from the zero-point level of SI' Provided that the S2 - SI energy gap Llss is sufficiently large that there is a quasi-continuum of vibrational states ofSI> is 0 energetic with S2, assumptions (a), (b) and (c) leading to the values of kMH listed in Table 5.7 appear reasonably valid. A value of kMH ~ 10 12 S- I is obtained for all the compounds considered, with the exception of azulene and benzene, where the large S2 - SI energy gap Llss gives a small Franck-Condon factor F. These two compounds do not obey Kasha's rule and Vavilov's law, respectively, and they are discussed in §5.13 and §5.14. In several compounds Llss < Eo (= 4000 cm- I), the cross-over energy (§5.7) from dominant CH vibrations (E > Eo) to CC-stretching vibrations (E < Eo). The extrapolation of the Siebrand model, which is based on a large energy gap and a quasi-continuum of CH vibrational modes, to Llss < Eo is questionable. The reduced density of SI vibronic states and the possible incidence of parity and symmetry considerations will tp.nd to reduce kMH' so that the values estimated in Table 5.7 represent upper limits. Hoytink2. 52 has observed S2 - So fluorescence in pyrene and 3: 4-benzopyrene, and has estimated an S2 - SI internal conversion rate of kMH ~ 2 X 10 12 S-I for pyrene. It is significant that these are two compounds in which Llss < Eo. Thermal repopulation of S2 from SI (rate kHM ~ 10 7 S-I for pyrene) contributes substantially to the S2 - So fluorescence intensity.2

5.13 Dual luminescences

Kasha's rule 4 states that the luminescence of an aromatic molecule occurs only from the lowest excited electronic state of a given multiplicity, so that SI - So fluorescence and TI - So phosphorescence are the only two molecular luminescences to be expected. This rule, which was never intended to be taken as absolute,19 has nevertheless proved a remarkably accurate generalization to date. There are numerous cases in which a molecular system, which contains only one aromatic molecular species, exhibits dual luminescences, i.e. two fluorescences and/or two phosphorescences, but few of these represent exceptions to Kasha's rule. (i) Excimers The molecular fluorescence spectrum FM(V) of an excited aromatic molecule IM* is normally observed in dilute fluid solution. If the molar concentration [1M] of the solution is increased, a second structureless fluorescence band FD(V) commonly appears at longer wavelengths, which is the emission of excimers (lD*) formed by the intermolecular process, (2.6)

5.13 Dual Luminescences

163

A pure aromatic liquid (e.g. benzene) may emit both molecular (lM*) and excimer (lD*) fluorescence, and either or both emissions may occur in the fluorescence spectrum of a pure aromatic crystal. The molecular phosphorescence spectrum PM(ii) of an excited aromatic molecule 3M* may be observed in dilute viscous fluid solution. In some compounds, e.g. naphthalene, a second structureless phosphorescence band PD(ii) has been detected in more concentrated solutions, which is attributed to the emission of triplet excimers eD*) formed by the intermolecular process (2.6a) The dual fluorescences and phosphorescences which occur due to intermolecular excimer formation are discussed in Chapter 7. They do not conflict with Kasha's rule, since the excimer (lD*, 3D*) differs from the excited molecule (I M*, 3M*). (ii) Molecular complexes and exciplexes

An unexcited aromatic molecule 1M in fluid solution may interact with an unexcited molecule lQ of another species to form a donor-acceptor complex, , (2.7b) In an excited state lE* or 3E* the complex may emit fluorescence or phosphorescence which differs from the molecular fluorescence or phosphorescence of IM* or 3M*. Alternatively, the complex IE may be dissociated in its ground state, but associated in one or both of its excited states lE* or 3E*. The exciplex states IE* or 3E* may be formed in fluid solution by the processes IM*+IQ~IE*

3M*+ lQ

~

3E*

(2.7) (2.7a)

The dual fluorescences and phosphorescences resulting from complex and exciplex formation are discussed in Chapter 9. They do not conflict with Kasha's rule, since IE* and 3E* differ from IM* and 3M*. (iii) Di-aromatic molecules

Kasha's rule is restricted to aromatic molecules which contain a single conjugated 7T-electron system. It does not apply to a molecule X-A-Y, which contains two (or more) aromatic groups X and Y, joined by a saturated (e.g. alkane) structure A. The absorption spectrum ofX-A-Y is similar to that of an equimolar mixture of X and Y showing that X and Y function as separate chromophoric groups. X-A-Y exhibits two

Radiationless Transitions 5.13

164

fluorescences, characteristic of IX':' and Iy*, respectively, and the ratio IFx/I Fy of their intensities depends on the fluorescence quantum yields and that there is strong spin-orbit-coupling to the two states (§6.13). If this is so, kTM and qFM might be sensitive to temperature or to a solvent shift of the energy levels. Figure 5.4 summarizes the suggested energy level scheme

Radiationless Transitions 5.13

168

and estimated rates of the various transitions in azulene. The scheme is tentative pending improved data on the triplet energies and SI - So, SI - Tq and TI - So transition rates (see p. 626, note b). 28 3kK

52 _...,-_ _..,-.=.::..::..c -

f

-284kK

~-"-----=r--

Tq

1-1--l: = 5·7 x lOB

I I

I SI

I 1

I 14 1 9 xld 2xl0 1

I I I I

tI I I t

-14 kK

T2

84kK

T,

I I

00'[6 "0']

So

Figure 5.4 Azulene. Proposed energy level scheme

and estimated rates of transitions. Solid lines, radiative transitions; broken lines, radiationless transitions

(vii) Biphenylene Hilpern28 reported fluorescence and phosphorescence emissions from biphenylene in solution, which she attributed to S2 - So and T2 - So transitions, respectively, since the energies exceeded the So - SI absorption energy. Birks et al.,29 using a specimen ofbiphenylene from the same source, confirmed the so-called S2 - So emission, and they also observed a weak SI - So fluorescence emission, whose spectrum is approximately the mirror image of the So - SI absorption spectrum. Munro et al.,30 using zonerefined specimens of biphenyl ene, showed that the apparent S2 - So and T2 - So emissions were due to an impurity, probably biphenylene oxide. In boric acid glass solution they observed SI - So fluorescence and also TI - So phosphorescence (ET = 19,000 em-I, 'TT = 1·5 s). Hochstrasser and McAlpine,31 also using zone-refined biphenylene, were unable to detect any luminescence, apart from a weak SI - So fluorescence ( k yM . However, Lawson et al. 39 observed that the limiting value of «(3Fh for large [Y] is identical to the value ((3F)max (=qMH) obtained with added [Q), which is consistent with (S.48b), which considers energy transfer to occur only from SI' Solvent-solute transfer or quenching in aromatic liquid solutions excited into SI is due to solvent excitation CM*) migration and solute diffusion, culminating in collisional transfer or quenching (§ 11.11). The rate parameter of IM* transfer to PPO, kYM ' ~ kOM' the rate parameter of IM* quenching by oxygen (Table 11.13). If similar S3 (lM**) solvent excitation migration occurred, it would be expected that the rate parameter of IM** transfer to PPO, k YH ~ kOH' the rate parameter of IM** quenching by oxygen, and that kYH (~kOH) > k YM (~kOM)' Inclusion of k YH in the reaction kinetic scheme predicts an increase of «(3Fh with [Y], since internal conversion in Y occurs with unit quantum efficiency. Inclusion of kOH in the reaction kinetic scheme predicts a decrease of «(3F)O with increase in [Q), which is contrary to the observed behaviour. It is concluded that the experimental data provide no evidence for IM** migration, leading to either transfer or quenching, but that they are consistent with the model of Lawson et al. 39 A liquid or solution either saturated with oxygen at 1 atm or containing O'IS M CC1 4 is considered adequate 39 . 41 to establish appropriate conditions to determine ((3F)max = qMH' Lawson et al. 41 used this technique to determine qMH, the quantum efficiency of internal conversion from S3 (Aex = 1849 A) to SI for benzene, toluene and p-xylene in various solvent environments. Their data are listed in Table S.9. In non-aromatic solvents the values are for 10-20 % solutions. Corrections for solvent absorption were applied in appropriate cases (isopropanol, tetrahydrofuran , ethyl ether).

5.14 Internal Conversion in Benzene and its Derivatives

175

The values of qMH for benzene show a remarkable dependence on the solvent environment: 0·45 in benzene, O· 37-0·28 in alcohols and other polar solvents, 0·25-0·22 in aliphatic hydrocarbons, 0·04 in a saturated fluorocarbon, and""() in the vapour phase. Lawson et al. 41 have noted a correlation between the magnitude of qMH and the intensity of the 'Ham band'. The latter is a weak low-energy absorption band observed in pure benzene and in benzene in solution in tetrahydrofuran, ethyl ether and acetonitrile, and more weakly in solution in cyclohexane. 42 - 43 The Ham band is assigned to the symmetry-forbidden 0 - 0 absorption transition to the SI (IB2u ) state of benzene, which is absent from the low-pressure vapour absorption spectrum (§I.4). Koyanagi 43 proposed that the enhancement of the 0 - 0 band in solution is due to a solvent perturbation which is effective in mixing the S3 (IE 1u ) and SI (I B 2u ) states of benzene. Related solvent perturbation effects are observed in the fluorescence and absorption spectra of benzene (§4.12, Figure 4.9). The S3 - SI radiationless transition is forbidden in the vapour phase (Table 5.9). The correlation between the probabilities ofthe So - SI 0 - 0 radiative transition and the S3 - SI internal conversion transition in solution indicates that solvent-perturbed S3 - SI mixing plays an important role in the latter process, probably by modifying the factor PCMH in the rate parameter (5.43) Current theories of radiationless transitions require revision to take account of the solvent perturbation effects so clearly demonstrated in benzene (Table 5.9). In toluene and p-xylene the substituent methyl groups internally enhance the 0 - 0 absorption intensity,44 and the increased values of qMH observed for these compounds are consistent with this. Dilution of the pure liquid with an inert solvent (e.g. cyclohexane) increases (3F for all the compounds studied, except benzene in which (3F decreases on dilution. 38 Birks et al.38 have proposed a model to account for this dependence of (3F on PM] in terms of the formation of higher excited states of excimers (5.50) which have a quantum efficiency, qOh of internal conversion to ID*, which is less than qMH (except in benzene). If m' and d' are the fractions of excited species in IM** and ID"'*, respectively, then the overall quantum efficiency of internal conversion is (5.51) Dilution reduces d and increases m', producing an increase in qIC' The behaviour of benzene is explained by assuming qMH < qOJ , so that qIC t

176

Radiationless Transitions 5.14

decreases on dilution. Taking the dynamic equilibrium conditions (§7.5), which are applicable in aromatic liquids and their concentrated solutions at room temperature, the following expression is derived for f3F from the reaction kinetic scheme 38

f3 - kMH + kOJ KJH [1 M] F -

kH

+ kJKJH[1M]

(5.52)

where kMH (koJ) are the rates of IM** (ID**) internal conversion to IM* (ID*); kIH (kIJ) are the rates of IM** (ID**) internal quenching; kJH [1M] and kHJ are the rates of 1 D** formation and dissociation, respectively (5.50); kH = kMH + k IH ; kJ = kDJ + kIJ; and KJH = kJH!k HJ . The ratio 1JFO!1JFM of the 1D* and 1M* fluorescence yields is predicted to be independent of the excitation wavelength Aex under dynamic equilibrium conditions, as is observed. 38 , 41 Observations of the dependence of f3F on [1M] for solutions of benzene, toluene, p-xylene and 2-methylnaphthalene in cyclohexane at different Aex have been analysed in terms of (5.52), and the values of qMH (=kMH!k H), qDJ (= kDJ!kJ) and (kJ!kH)KJH thus obtained are listed in Table 5.10. No corrections were applied to the experimental values of f3F for photoproduct quenching (5.48), but the influence of [X] may not be too important at longer wavelengths and lower values of [I M], and in compounds other than benzene. Lawson et aIY have given an alternative qualitative explanation of the changes in f3F on dilution by cyclohexane in terms of two opposing effects, (i) a reduction in the concentration [X] of photoproduct quencher, giving an increase in f3F' and (ii) a decrease in qMH (and hence in {3F) in changing from an aromatic to an aliphatic solvent environment. Further studies are required to distinguish the models of Birks et aI.38 and Lawson et al.,41 which are not mutually exclusive. The relative roles of the photophysical product 1D **, the photochemical product X, and the solvent environment, will depend on the nature of the parent molecule 1M and on the excitation wavelength Aex and temperature, and it would b,e unwise to attempt to generalize from the limited available data. The absence of S3 - SI internal conversion in benzene vapour and other photophysical properties of benzene and its alkyl derivatives in the vapour phase are discussed in §6.16. When benzene in dilute solution in hexane at room temperature is excited into Sl> four processes comp.ete for its excitation energy: (i) fluorescence, rate constant kFM = 2·1 X 106 S-I (Table 5.1); (ii) internal conversion, rate constant k~M ~ 0·5 X 106 S-I (Table 5.5); (iii) temperature-independent intersystem crossing, rate constant k~M (= k?M - k~M) = 12·8 X 10 6 S-I (Table 5.2); and

5.14 Internal Conversion in Benzene and its Derivatives

177

(iv) temperature-dependent internal quenching, rate constant kUM (= kIM - k?M) = 23·8 x 10 6 S-I (Tables 5.1 and 5.2), with frequency factor kiM = 1·2 X 10 12 S-I, W1M = 0·35 eV. The benzene vapour data (§6.16) indicate that (iv) corresponds to an efficient S I - So internal conversion process, via an isomeric state of benzene, which gives a small photochemical yield CPCM of the isomer. Thus for excitation into Sh the respective quantum yields are (CPFM)I = 0'054, (CPGM)I c:: 0·013, (CPTM)I c:: 0'326, (CPUM)I + (CPCM)I c:: 0·607. Lumb et al. 45 have observed the fluorescence and phosphorescence excitation spectra of rigid solutions of benzene in EOA (3: 3: 1, ether; iso-octane; alcohol) at 77°K. The two excitation spectra are identical, showing that CPFM and CPTM (oc CPPT) vary in the same manner with;\'ex- For a 0'112 M solution, fJF (5.45) decreases below unity at ;\.ex < 243 nm (=41,200 em-I). The 0 - 0 So - SI transition energy of benzene is 38,400 cm- I (Table 3.1), so that the decrease of fJF corresponds to the onset of the isomeric internal conversion process (iv) of activation energy W1M = O' 35 eV (=2800 em-I = 41,200 - 38,400 cm- I). In low pressure vapours where vibrational relaxation is inhibited, the threshold energy of this process is sharp (§6.16). In solution it is blurred by the competing vibrational relaxation. These results indicate that at ;\.ex < 243 nm, CPFM and CPTM (and probably CPGM), being processes originating from the lower and zero-point vibrational levels of Sh decrease together to a minimum at ;\.ex = 210 nm, while the competing process (iv) which originates from the higher vibrational levels of SI increases in probability, so that CPUM and CPCM increase. The fluorescence quantum efficiency of polystyrene depends on excitation wavelength in a similar manner to that ofbenzene,48, 49 indicating that the deviation from Vavilov's law is an inherent property of the benzene molecular structure. Further studies are required to elucidate the observed wavelength dependence of (CPF)ex in naphthalene and its derivatives,38 which may be photochemical in origin. The photo-isomerization of benzene originates from vibrational distortions of the planar ring structure, a property which appears to be specific to benzene and its simple derivatives and not common to the higher condensed aromatic hydrocarbons. The temperature dependence of the triplet lifetime of benzene, which differs from that of the higher condensed hydrocarbons, is also attributed to vibrational distortions of the molecule (§6.17).

Radiationless Transitions

178

Table 5.1 Rate parameters of internal quenching and fluorescence of aromatic compounds in dilute deoxygenated solution at room temperature (derived from data of Table 4.5) k iM

Code

Compound Benzene

Id 1A

Benzene'd 6 Toluene

lAd 1C lD

Toluene'd s o-Xylene m-Xylene p-Xylene

lDd 1E

p-Xylene'd lO Mesitylene

IF 1G IH 2

Hexamethylbenzene 1,2,4-Trimethylbenzene Ethyl benzene Naphthalene

2d 2A

Naphthalene'd g 1-Methylnaphthalene

2B

2-Methylnaphthalene

2C

1,6-Dimethylnaphthalene

2D

2,6-Dimethylnaphthalene

2E 2X 2Y 2Z 3.1

2,3-DimethyInaphthalene 1-Methoxynaphthalene 2-Methoxynaphthalene Acenaphthene Anthracene

lB

kFM

Solvent

(l06 S-I)

(l06 S-I)

Hexane Hexane Cyclohexane Ethanol Cyclohexane Hexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Hexane Hexane Cyclohexane Cyclohexane Hexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Ethanol Hexane 95 % EtOH Cyclohexane Cyclohexane 95 % EtOH Cyclohexane 95% EtOH Heptane 95 % EtOH Cyclohexane 95% EtOH Cyclohexane Toluene Toluene Cyclohexane Benzene (mean) Cyclohexane Alcohol Ethanol 95% EtOH

37'1 21 '0 32'5 31'0 35'3 34'5 22'1 23-6 26'1 27-9 28'3 24'6 22-3 25 '9 34'7 23 '6

2'1 1'2 2'0 1"35 2'5 3'0 4'2 5'0 4'9 4'6 7'1 6'2 11'1 7'2 3'3

~160

24'2 27-4 8-4 6'7 7'5 6'9-7-8 17 8'1 11-8 21 12-4 17'6 15'0 14-4 16'5 16'2 8'8 11

39 10'9 180 143 173 127 140

SI 1Lb

'L b lLb

lLb

'L b 'L b 1Lb

1Lb 1Lb

3-9 ~3'3

lLb

12'6 4'9 2'0 1'6 2'0 1"6-1'85 2'3 2-3 H 2'9 4'5 3'4 5'0 3'6 9'9 6'8 4'1 28 28 10'9 63-3 60'2 48 '8 54'6 52'1

1Lb 1Lb lLb

1Lb lLb

ILb

1Lb

1Lb

1Lb 1Lb 1Lb lLb lLa

Radiationless Transitions

179 Table 5.1 (continued)

Compound

Code 3.1d 3.1A

Anthracene'd lO 9-Methylanthracene

3.1B 3.1C

9,10-Dimethylanthracene 9,10-Diphenylanthracene

3.1D

9-Phenylanthracene

3.2

Phenanthrene

4.1

Pyrene

4.2

Tetracene

4.3 4.3G 4.3H 4.3L 4.4 4.6 4'6d 5.1

1 :2-Benzanthracene (BA) 5-Methyl BA 6-Methyl BA 10-Methyl BA Chrysene Triphenylene Triphenylene'd!2 Perylene

6.8 7.2 8.2 9.2 A Ad B D

Hexahelicene Heptahelicene Octahelicene Nonahelicene Biphenyl Biphenyl'd lO Fluorene p-Terphenyl

Dd E

p-Terphenyl'd I4 p-Quaterphenyl

F G

Fluoranthene Azulene (S2 - So fluorescence) Rubrene

H 7

Solvent Cyclohexane Cyclohexane Alcohol Alcohol Alcohol Benzene Benzene Cyclohexane Alcohol Heptane Isobutanol Cyclohexanol Cyclohexane Ethanol Ethanol Cyclohexane Cyclohexane Benzene Benzene Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Benzene Ethanol Dioxan Dioxan Dioxan Dioxan Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Cyclohexane Benzene

kiM

kFM

(10 6 S-I)

(10 6 S-I)

SI

150 154 137 33'6 23'5 20'5 21-7 91 108 14.1 12'5 12'5 0'75 0'7 0'53 129 90 161 152 17-8 18'3 15'5 13'9 19'8 25'5 24'0 22'4 21-7 66 71 98 101 53'1 48'8 33'6 242 120 180 248 325 260 18'9 570

54'4 63'7 54'6 57'1 124 118 112 62'5 88'5 2'7 3'3 4'0 1'45 1-37 1'36 27 19 31 29 4'3 4'7 2:5 4'6 2'6 1'8 2'4 180 145 2'9 1'5 1'4 1'5 9'3 8'1 67 820 710 590 807 926 740 4'7 143

IL. IL.

(k lH )

(kFH)

-0

61

IL. IL.

IL. 1Lb

1Lb

IL.

1Lb 1Lb 1Lb 1Lb 1Lb

ILb 1Lb IL. 1Lb

ILb 1Lb 1Lb 1Lb 1Lb IL. IL.

IL. IL. 1Lb

ILa (S2) ILa

Radiationless Transitions

180

Table 5.2 Frequency factors and activation energies of internal quenching of fluorescence of aromatic molecules in dilute solution k~M

Code

Compound Benzene

IA

Toluene

1D

p-Xylene

2

Naphthalene

2d

Naphthalene-d 8

2A

I-Methylnaphthalene 2-Methylnaphthalene I,6-Dimethylnaphthalene

2B 2C 2Q 3.IA 3.1Ad 3.1H 4.1

l-Chloronaphthalene 9-Methylanthracene 9-Methylanthracene-d 1 2 9,10-Dichloroanthracene Pyrene

4.1d

Pyrene-d lO

4.1E 5.6

3-Bromopyrene 1 :2: 3 :4-Dibenzanthracene

k;M (l08 S- I)

W 1M (eV)

3-9

1-2 x 104 I-2 x 10 3 8 x 10 2 47-2 2 x 10 3 8-1 8-1 0"4 1-J 0'55 0-27

0·35 0-22 0-23 0-18 0-25 0-11 0-11 0-06 0-08 0-03 0-047

k

3-5

0-20

0-041

k

0-83

0-034

d

0"41

0-024

d

2-7 0'76

0-11 0-04

e d

Solvent

(10 6 S-

Hexane Ethanol Hexane Hexane Ethanol Hexane Ethanol Hexane Ethanol 95 % EtOH Polymethylmethacrylate Polymethylmethacrylate 95 % EtOH

13 -3

8-6 13-8 12-8 8-6 14-2 14-5 2-7 1-5

95 % EtOH

I)

Ref. a a a b a a a a c d

Heptane 95 % EtOH

11-6

Ethanol

73

36

0-07

c

Ethanol Lucite

~O

~O

50 6

1-10 0-08

f

Ethanol

~O

30

0-10

f

Ethanol Lucite

~O

~O

30 120

0-10 0-17

f f g,h g

Ethanol Liq. paraffin Paraffin oil Nonane Polymethylmethacrylate Polymethylmethacrylate Ethanol Polymethylmethacrylate

« 0-22 0 0 0 0"43

0-33 0-8 1-3 0-06 0-069

0-1 0-13 0-08 0-05 0-06

0-30

0-08

0-054

64 0-22

0-076 0'047

52 7'7

f

j

I

h

Radiationless Transitions

181 Table 5.2 (continued)

k?M

5.7 5.8 6.2 8.4

kiM

W1M

Compound

Sol,;vent

(10 6 S-I)

1 :2:5:6-Dibenzanthracene 1 :2:7 :8-Dibenzanthracene 1: 12-Benzoperylene 1 :2-Benzocoronene

Polymethylmethacrylate PolymethyImethacrylate Polymethylmethacrylate Polymethylmethacrylate

16'8

0'12

0'032

3'3

0'064

0'035

0'1

0'042

0'076

0'064

Code

. 2'55 1'40

(l08

S-I)

(eV)

Ref.

References J. R. Greenleaf and T. A. King, Proc. Intern. Can! Luminescence, Budapest (1966). J. R. Greenleaf, M. D. Lumb and J . B. Birks, J. Phys. B. , 1, 1157 (1968). B. Stevens and M. Thomaz, Chem. Phys. Lett., 1, 549 (1968). B. K. Selinger, Austral. J. Chem., 19, 825 (1966). J. B. Birks and T. A. King, Proc. Roy. Soc. A, 291, 244 (1966). R. G. Bennett and P. J. McCartin, J. Chem. Phys., 44, 1969 (1966). B. Stevens, M. F. Thomaz and J. Jones, J. Chem. Phys. , 46, 405 (1967). B. Stevens and M. Thomaz, Chem. Phys. Lett., 1, 535 (1968). E. Doller and Th. Forster, Z. Phys. Chem. (N.F.), 34, 132 (1962). j. Th . Forster and H. P. Seidel, Z . Phys. Chem. (N.F.), 48, 58 (1965). k. P. F. Jones and A. R. Calloway. Transitions Non Radiatives dans les Molecules, Paris, 1969; J. Chim. Phys. (in press) (observations of k~M ' k~M and WTM ). I. J. L. Kropp and W. R. Dawson, Molecular Luminescence, p. 39 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. a. b. c. d. e. f. g. h. i.

Radiationless Transitions

182

Table 5.3 Energies (Er) and lifetimes (TT) of the lowest triplet state (Tl)' and Tl - So intersystem crossing rates (kGT) of aromatic hydrocarbons 8

Code

Compound

TJ

ET (em-I)

1 1d 2 2d 3.1 3.1d 3.2 3.2d 4.1 4.1d 4.2 4.3 4.3d 4.4 4.4d 4.5 4.6 4.6d 5.2 5.7 5.9 5.14 6.8 6.11 7.1 7.5

Benzene Benzene'd 6 Naphthalene Naphthalene'd B Anthracene Anthracene·d lo Phenanthrene Phenanthrene·d I0 Pyrene Pyrene·d lo Tetracene 1 :2-Benzanthracene 1 :2-Benzanthracene'd I2 Chrysene Chrysene'd 12 3: 4-Benzophenanthrene Triphenylene Tripheny1ene'd 12 1 :2-Benzopyrene 1: 2: 5: 6-Dibenzanthracene Picene 3 :4: 5: 6-Dibenzophenanthrene Hexahelicene 1 :2: 6 :7-Dibenzopyrene Coronene 1 :2:3:4:5:6:7:8-Tetrabenzanthracene 1: 12:2: 3: 10: lI-Tribenzoperylene 1 :2:3 :4:6 :7: 12: 13-Tetrabenzopentacene 1 :2: 3 :4: 5: 6: 10: ll-Tetra-

0·500 0'500 0-445 0·445 0·417 0·417 0'417 0'417 0·385 0·385 0·400 0-400 0·400 0·400 0·400 0-400 0·400 0·400 0·375 0·389 0·389 0'389 0·380 0·368 0'333 0·375

29500 29500 21300 21300 14700 14700 21600 21600 16900 16900 10300 16500 16500 20000 20000 20000 23300 23300 18500 18300 20100 19800 19000 20400 19100 20550

8.5 9.3 10.2

TT

(s)

kGT

(S-I)

16 0·029 26 0·0050 2·4 0·39 0·020 19 0·045 22 0·14 7·1 0·25 3·5 0·029 16 0·5 2·0 3·2 0·29 0·008 130 0·3 3·3 1·7 0·59 2·6 0·36 13 0·043 2·5 0·37 0·029 16 22 0·012 0·47 2·0 1·5 0·67 2·5 0·37 2·5 0·37 2·1 0·43 7·5 0'10 9·0 0·077 8·9 0·082

Ref. a a b-o d,g,i,k,n d, 0, r r, s b, c, e-i, k-m, t g, i b,c, g, t, u g

v, w b, c, f, t, u s b, c, e, m, 0, t x t b, d, g, i, k, m, t g, i t, A b, c, t t, A t z t b,d,e t,A

0·348 18600

3·3

0·27

A

0·357 19600

8·4

0·089

A

0·333 18600

4-4

0·20

A

0·344 19160

3·3

0·27

A

0·300 17540

3-8

0·23

A

0·22 0·057 0·17 0·67 0·36 0·16 1·2 0·21 0'17

e,g, h,k,o,q g,h b,c,e, m,q p g, t

benzantha~threne

11.1 13.1 A Ad B C D Dd F J K

5 :6: 8:9: 14: 15: 17: 18-Tetrabenzoheptacene 1:12:2:3:4:5:6 :7:8:9:10 : 11Hexabenzocoronene Biphenyl Biphenyl'd lo Fluorene Biphenylene p-Terphenyl p-Terphenyl'd I4 Fluoranthene m- Terphenyl 1,3,5-Triphenylbenzene

0·455 0'455 0·435 0·400 0·438 0·438 0·385 0·438 0·428

22900 4·0 22900 11 23800 5·0 19000 1·5 20600 2·6 20600 5·3 18500 0·85 22700 4·1 22600 5·0

g

e, t Y d, t, Y

183

Radiationiess Transitions Table 5.3 (continued) References

a. M. R. Wright, R. P. Frosch and G. W. Robinson, J. Chern. Phys., 33, 934 (1960). b. D. S. McClure, J. Chern. Phys., 17, 905 (1949). c. D. P. Craig and I. G. Ross, J. Chern . Soc., p. 1589 (1954). d. M. S. de Groot and J. H. van der Waals, Mol. Phys., 3, 190 (1960); 4, 189 (1961). e. G. von Foerster, Z. Naturforsch., 18a, 620 (1963). f. J. Czekalla, G. Briegleb, W. Herre and H. J. Vahlensieck, Z. Elektrochern., 63, 1197 (1959). g. R. E. Kellogg and R. P. Schwenker, J. Chern. Phys., 41, 2860 (1964). h. V. L. Erinolaev, Izv. Akad. Nauk SSSR, Ser.jiz., 27, 619 (1963). i. E. C. Lim and J. D. Laposa, J. Chern. Phys., 41, 3257 (1964). j. J. W. Hilpern, G. Porter and L. J. Stief, Proc. Roy. Soc. A, 277, 437 (1964). k. T. Azumi and S. P. McGlynn,J. Chern. Phys., 39,1186 (1963). I. D. Olness and H. Sponer, J. Chern. Phys., 38, 1779 (1963). m. P. P. Dikun, A. A. Petrov and B. V. Sveshnikov, Zh. Eks. Teor. Fiz., 21, 150 (1951). n. S. Siegel and H. S. Judeikis, J. Chern. Phys., 42,3060 (1965). o. G. N. Lewis and M. Kasha,J. Arn. Chern. Soc., 66, 2100 (1944). p. I. H. Munro, T. D. S. Hamilton, J. P. Ray and G. F. Moore, Phys. Lett., 20, 386 (1966). q. V. V. Trusov and P. A. Teplyakov, Opt. Spektrosk., 16, 52 (1964). r. A. Beckett, Nature, 211, 410 (1966). s. W. Siebrand and D. F. Williams, J. Chern. Phys., 46, 403 (1967). t. E. Clar and M. Zander, Chern. Ber. , 89, 749 (1956). u. B. Stevens and M. S. Walker, Proc. Roy. Soc. A, 281, 420 (1964). v. S. P. McGlynn, M. R. Padye and M. Kasha, J. Chern. Phys., 23, 593 (1955). w. A. A. Lamola, W. G. Herkstroeter, J. C. Dalton and G. S. Hammond, J. Chern. Phys., 42, 1715 (1965). x. R. E. Kellogg and R. G. Bennett, J. Chern. Phys., 41, 3042 (1964). y. J. S. Brinen, J. G. Koren and W. G. Hodgson, J. Chern. Phys., 44,3095 (1966). z. W. Rhodes and M. F. A. El-Sayed, J. Mol. Spectrosc., 9, 42 (1962). A. M. Zander, Phosphorirnetry, Academic Press, New York, 1968.

Radiationless Transitions

184

Table 5.4 Energies and energy gaps (in 10 2 cm- I) of lower excited states of

aromatic hydrocarbons Code

Compound

1 2 3.1 3.2 4.1 4.2 4.3 4.4 4.5

Benzene Naphthalene Anthracene Phenanthrene Pyrene Tetracene 1 : 2-Benzanthracene Chrysene 3:4-Benzophenanthrene 4.6 Triphenylene 5.1 Perylene 5.2 1 : 2-Benzopyrene 5.3 3 : 4-Benzopyrene 5.4 Pentacene 5.5 1: 2-Benzotetracene 5.6 1 :2:3 :4-Dibenzanthracene 5.7 1: 2: 5: 6-Dibenzanthracene 5.8 1 :2:7:8-Dibenzanthracene 5.9 Picene 5.10 1:2-Benzochrysene 5.11 5:6-Benzochrysene 5.12 1 :2-Benzotetraphene 5.13 3:4-Benzotetraphene 5.14 3: 4: 5: 6-Dibenzophenanthrene 5.1 5 Pentaphene 6.1 Anthanthrene 6.2 1: 12-Benzoperylene 6.3 1 : 2-Benzoperylene 6.4 2: 3-Benzoperylene 6.6 ] : 2-Benzopentacene 6.7 Hexaphene 6.8 Hexahelicene 7.1 Coronene 8.1 Bisanthrene 9.1 1: 14-Benzobisanthrene 10.1 Ovalene B Fluorene C F G

Biphenylene Fluoranthene Azulene

3L.

ILb

IL.

ET

Es

LIsT

Llss

(lL. - 3L.)

295 213 147 216 169 103 165 200 200

384 480 295 322 350 213 267 147 289 342 216 269 299 169 212 103 260 279 165 277 314 200 270 303 200

384 322 267 289 269 212 260 277 270

89 109 120 73 100 109 95 77 70

96 28

185 137 120 ]26 130 109 114 114 103

233 126 186 ]47 77

233 126 186 147 77

299 66 230 104 272 86 247 100 171 94 223 178 267 89

53

299 352 230 272 301 247 260 233 171 223 178 267 286

53 30 19 37 33

29 13 62

119 104 115 113 94

19

108

]83 253 286 183 253

70

33

103

185 254 286 183 254

69

32

101

208 266 308 208 186 270 300 186 198 259 3]2 198 249 269

266 270 259 249

58 84 61

42 30 53 20

100 114 114

255 274

255

19

]98 253 304 198 253

55

5]

106

170 236 281 231 161 246 258 295 199 313 230 182 214 227 190 242 273 191 238 283 236 151 187

66

45

109

85

12 96 83

97

238 (T I) 190 185 84

170 236 231 161 246 199 230 ]82 190 242 191 238 ]51 187

215 219 332 382 238 332 (SI)

52 47

13 31 45 85

83 92

4 50

144

65 26 68 26 58 141

91 94 199

94

(S2)

255 281 190 255 253 279 185 253 142 283 84 142

Radiationless Transitions

185

Table 5.5 Estimated rate constants of SI - So internal conversion (k GM ) kGM

Code

Compound

1 Id 2 2d 3.1 3.1d 3.2 3.2d 4.1 4.1d 4.2 4.2d 4.3 4.3d 4.4 4.4d 4.5 4.5d 4.6 4.6d 5.1 5.1d 5.2 5.2d 5.3 5.3d 6.1 6.1d 7.1 7.1d 0 Od

Benzene Benzene·d. Naphthalene Naphthalene·d s Anthracene Anthracene·d 10 Phenanthrene Phenanthrene·d lo Pyrene Pyrene·d lo Tetracene Tetracene·d l2 1 : 2-Benzanthracene 1 :2-Benzanthracene·d 12 Chrysene Chrysene·d 12 3: 4-Benzophenanthrene 3 : 4-Benzophenanthrene·d I2 Triphenylene Triphenylene·d 12 Perylene Perylene·d 12 1 :2-Benzopyrene 1: 2-Benzopyrene·d 12 3 : 4-Benzopyrene 3 : 4-Benzopyrene·d I2 Anthanthrene Anthanthrene·d 12 Coronene Coronene·d l2 Azulene Azulene·d s

1J

Es (10 2 em-I)

0·5

384

0·445

322

0·417

267

0·417

289

0·385

269

0·40

212

0·40

260

0·40

277

0·40

270

0·40

299

0·375

230

0·375

272

0·375

247

0·353

231

0·333

234

0·445

142

(10· S-I) (10· S-I) (ref. 18) kGM

F

10-s 0·04 6 x 10- 11 0·0003 3 x 10- 8 0·12 10 5 x 100·002 2·5 x 10- 7 1·0 10- s 0·04 7 x 10- s 0·3 1·8 x 10- 9 0·007 7 x lO- s 0·3 1·8 x 10- 9 0·007 4 x 10-· 16 5 x 10- 7 2 2 x 10- 7 0·8 lO- s 0·04 8 x lO- s 0·3 2 x 10- 9 0·009 7 100·4 3·5 x 10- 9 0·014 2 x IO-B 0·07 3·5 x 10- 10 0·001 7 6 x 102·4 1·3 x lO- s 0·05 4 x lO- s 0·16 10-9 0·004 7 2·2 x 100·9 lO- s 0·04 2·5 x 10- 7 1·0 4 x 10- 9 0·016 7 100·4 10- 9 0·004 6 x 10- 4 2·5 X 103 3 x 10- 4 1·2 x 103

t Recalculated from (5.42). Original value ls of 3 x 104 S-I is incorrect.

0·5 0·2 1·0 0·2 0·3t 20 0·6 0·2

0·07 3

1·0 0·5 6

X

103

Radiationless Transitions

186

Table 5.6 Fluorescence and phosphorescence transition probabilities (data from Tables 4.5,6.2 and 6.2A)

Code

Compound

2 2d 3.2 4.4d 4.6 4.6d 5.6 5.7 5.8 7.1 7.1d 8.4

Naphthalene Naphthalene'dB Phenanthrene Chrysene'd 12 Triphenyiene T riphenyiene' d 12 1: 2: 3: 4-Dibenzanthracene 1: 2: 5: 6-Dibenzanthracene 1:2:7 :8-Dibenzanthracene Coronene Coronene'd 12 1: 2-Benzocoronene

kFM

k pT (S-I)

kFM/k pT (10B)

2'0

0'02 0'041 0'031 0'032 0'031 0'028 0'045 0'030 0'022 0'017 0'017 0'025

1'0 0'6 1'0 0'8 0'6 0'9 0'5 1'3 0'6 0'5 0'5 0'4

(10 6 S-I)

2-3

3'0 (2'6) 1'8

2'4 2'7 4'0 1'27 0'84 0'78 0'9

Radiationless Transitions

187

Table 5.7 Estimated (maximum) rate constants of S2 - SI internal conversion (kMH) kMH

Llss

Code

Compound

T)

1 2 3_2

Benzene Naphthalene Phenanthrene Pyrene 1 : 2-Benzanthracene Chrysene 3:4-Benzophenanthrene Triphenylene 1: 2-Benzopyrene 3 : 4-Benzopyrene

0-5 0 -445

4.1 4.3 4.4 4.5 4.6 5.2 5.3 7.1 G Gd

Coronene Azulene Azulene-d s

0-417 0-385 0 -40 0 -40 0-40 0 -40 0-375 0 -375 0 -333 0 -445 0 -445

(10 2 em-I) 96 28 53 30 19 37 33 53 29 13 45 141 141

F

(10 12 S-I)

0-01 0-3 0 -08 0-3

0:04 1-2 0 -3 1-2

0-4 0-16 0 -24 0 -075 0 -3

1-6 0 -6 1-0 0 -3 1-2

0-4 0 -25 0 -0006 0 -003

1-6 1'0 0 '0025 0 -0012

188

Radiationless Transitions

Table 5.8 Absorption (vp) and fluorescence (va, Vb) maxima of p -dimethylaminobenzonitrile in 10- 4 M solution in various solvents at room temperature 20 (energies in 10 2 em-I) Solvent

vp

iso-Octane iso-Pentane Cyclohexane Methylcyclohexane Decalin Tetralin Carbon tetrachloride Tetrachlorethane Benzene Dioxan Dibutyl ether Diethyl ether Trichlorethylene Chloro benzene Bromobenzene Benzylacetate 0- Dichlorobenzene Ethyl acetate Trifluorotoluene Butylchloride Methylene chloride Tetrahydrofuran Pyridine Acetanhydride Butyronitrile Acetone Cyclohexanol iso-Butanol iso-Propanol n-Propano] Ethanol Methanol Dimethyl formam ide

356 355 -5 355-5 355 -5 355-5 347-5 344 345 344-2 346 352-5 351-5 344 341 336 341 -5 348 '5 347 347'5 358 345 -5 339 339

Va

Weak 240'5 244-5 249 256 253 236-5 249 229 243 245 232 229-8 222 215 222-5

n.m. 338 342 348 -5 341-5 340 344-5

219 223 219-5 212 211 210-5 210-7

Vb

log (ha IIFb)

290-5 290-5 290-5 288-5 290-5 281 -5 281-5 282-5 283 -5 280-5 287 278-5 276-5 281'5 280 272-5 277 275-5 280 282'5 275 278 274

CJJ

275 276

CJJ CJJ CJJ CJJ CJJ CJJ CJJ CJJ

0-08 0'20 0-63-1 0-74-1 0'78-1 0-68-1 0-50 0-80-1 0 -72 0-95-1 0-87-1 0-46 0'28 0-27 0-67 0-76 0-76 0-64 0-86 0-65 1'00 0 -48

LJj

0-001 0-005 -0-001 - 0-001 0-012 0-031 0-01 0-002 0-002 0 -028 0-106 0-166 0 '124 0-143 0-128 0-142 0-185 0 -202 0-206 0-218 0-23 0-26 0-274 0-287 0-235 0 -273 0-28 0-288 0-308

189

Radiationless Transitions

Table 5.9 S3 (" = 1849 A) - SI internal conversion quantum efficiencies (qMH)41 Solute

Solvent environment

qMH

1

Benzene

lA

Toluene

1D

p-Xylene

Benzene Methanol iso-Propanol Tetrahydrofuran Ethyl ether Acetonitrile Hexane Cyclohexane Methyl cyclohexane Decalin iso-Octane Perfluorinated hexane Vapour (10 torr pressure) Toluene Cyclohexane p-Xylene Cyclohexane

0'45 0'37 0'33 0'33 0'32 0'28 0'25 0'24 0'24 0'24 0'22 0'04 < 10- 4 0-76 0'58 1'03 0'95

Code

Radiationless Transitions

190

Table 5.10 Internal conversion quantum efficiencies of deoxygenated cyclohexane solutions at different excitation wavelengths (,\e.)38 (kJ /kH)Km

'\ex

Code

Compound Benzene

lA

Toluene

ID

p-Xylene

2B

2-Methylnaphthalene

(nm)

qMH

qOJ

(M- 1)

195 200 205 210 195 200 210 220 195 200 205 210 195 200 205 210 215 220 230

0'28 0'31 0'35 0'44 0'73 0'78 0'84 0'93 0'91 0'97 0'985 1'00 1'00 1'00 1'00 1'00 1'00 1'00 1'00

0'48 0'56 0'56 0'62 0 0 0 0 0'1 4 0 0 0 0 0'06 0'10 0'13 0'16 0'16 0'10

0'26 0'26 0'22 0'20 0'055 0'041 0'027 0'011 0'11 0'053 0 '036 0'026 0'034 0'063 0'093 0'12 0'14 0'16 0'11

5.15 References

191

5.15 References 1. P. M. Rentzepis, (a) Chem.Phys. Lett., 2,117 (1968); (b)Photochem.Photobiol., 8, 579 (1968). 2. P. A. Ge\dof, R. P. H. Rettschnick and G. J. Hoytink, Chem. Phys. Lett., 4, 59 (1969). 3. J. B. Birks, Phys. Rev., 94,1567 (1964). 4. M. Kasha, Disc. Faraday Soc., 9, 14 (1950). 5. J. B. Birks, C. L. Braga and M. D. Lumb, Proc. Roy. Soc., A283, 83 (1965). 6. R. G. Bennett and P. J. McCartin, J. Chem. Phys. , 44, 1969 (1966). 7. W. Siebrand, J. Chem. Phys., 47, 2411 (1967). 8. W. Siebrand, The Triplet State, p. 31, Cambridge University Press, 1967. 9. M. Gouterman, J. Chem. Phys., 36, 2846 (1962). 10. G. W. Robinson and R. P. Frosch, J. Chem. Phys., 37,1962 (1962). 11. G. W. Robinson and R. P. Frosch, J. Chem. Phys., 38,1187 (1963). 12. G . R. Hunt, E. F. McCoy and 1. G. Ross, Austral. J. Chem., 15, 591 (1962). 13. W. Siebrand, J. Chem. Phys., 46, 440 (1967). 14. G. W. Robinson, J. Chem. Phys., 47, 1967 (1967). 15. M. Bixon and J. Jortner, J. Chem. Phys., 48, 715 (1968). 16. W. Siebrand, Chem. Phys. Lett., 2, 94 (1968). 17. E. F. McCoy and I. G. Ross, Austral. J. Chem., 15,573 (1962). 18. W. Siebrand and D. F. Williams, J. Chem. Phys., 49, 1860 (1968). 19. M. Kasha. Private communication (1967). 20. E. Lippert, W. Hider and H. Boos, Advances in Molecular Spectroscopy, p. 443, Pergamon Press, London, 1962. 21. M. Beer and H. C. Longuet-Higgins, J. Chem. Phys., 23, 1390 (1955). 22. G. Visnawath and M. Kasha, J. Chem. Phys., 24, 574 (1956). 23. J. W. Sidman and D . S. McClure, J. Chem. Phys., 24, 757 (1956). 24. Z. S. Ruzevich, Opt. Spectrosc., 15, 191 (1963). 25. G. Binsch, E. Heilbronner, R. Jankow and D. Schmidt, Chem. Phys. Lett., 1, 135 (1967). 26. R. C. Dhingra and J. A. Poole, Chem. Phys. Lett., 2, 108 (1968). 27(a). R. C. Dhingra and J. A. Poole, J. Chem. Phys., 48, 4829 (1968) ; (b) J. A. Poole and R. C. Dhingra, Molecular Luminescence, p. 813 (Ed. E. C. Lim), W. A. Benjamin Inc., New York, 1969. 28. J. W. Hilpern, Trans. Faraday Soc., 61, 605 (1965). 29. J. B. Birks, J. C. Conte and G. Walker, Phys. Lett., 19, 125 (1965). 30. I. H. Munro, T. D. S. Hamilton, J. P. Ray and G. F. Moore, Phys. Lett., 20, 386 (1966). 31. R. M. Hochstrasser and R. D. McAlpine, J. Chem. Phys., 44, 3325 (1966). 32. G. Walker, Unpublished results (1967). 33. R. V. Naumann, 131st Mtg. Am. Chern. Soc., Miami, Florida, April 1957; H. A. Ory, Ph.D. thesis, Louisiana State University (1957); J. H. Wharton, Ph.D. thesis, Louisiana State University (1962). 34. J. H. Wharton, H. A. Ory and R. V. Nauman, Private communication (1967). 35. D. Scott and R. S. Becker, J. Chem. Phys., 35, 516, 2246 (1961). 36. A. T. Armstrong, F . J. Smith, E. Elder and S. P. McGlynn, J. Chem. Phys., 46,4321 (1967). 37. C. L. Braun, S. Kato and S. Lipsky, J. Chem. Phys., 39, 1645 (1963). 38. J. B. Birks, J. C. Conte and G. Walker, J. Phys. B (Proc. Phys. Soc.), Ser. 2, 1, 934 (1968).

192

Radiationless Transitions 5.15

39. C. W. Lawson, F. Hirayama and S. Lipsky, Molecular Luminescence, p. 837 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. 40. U. Laor and A. Weinreb, J. Chem. Phys., 43,1565 (1965). 41. C. W. Lawson, F. Hirayama and S. Lipsky, J. Chem. Phys. , 51, 1590 (1969). 42. J. S. Ham, J. Chem. Phys. , 21, 756 (1953). 43. M. Koyanagi, J. Mol. Spectrosc., 25, 273 (1968). 44. J. Petruska, J. Chem. Phys., 34, 1120 (1961). 45. M. D. Lumb, C. Lloyd Braga and L. C. Pereira, Trans. Faraday Soc., 65, 1992 (1969). 46. P. F. Jones and A. R. Calloway, Transitions Non Radiatives dans les Molecules, Paris, 1969; J. Chim. Phys. (in press). 47. A. Kearvell and F. Wilkinson, Transitions Non Radiatives dans les Molecules, Paris, 1969; J. Chim. Phys. (in press). 48. J. B. Birks and K. N. Kuchela, Disc. Faraday Soc., 27,57 (1959). 49. A. Weinreb and M. Leibowitz, Mol. Cryst., 4, 15 (1968). 50. P. M. Rentzepis, 155th Nat. Mtg. Am. Chern. Soc., San Francisco, Abstract 91 (1968) (quoted in ref. 27(b)). 51. D. P. Chock, J. Jortner and S. A. Rice, J. Chem. Phys., 49, 610 (1968). 52. G. J. Hoytink, private communication (1969).

6 The triplet state 6.1 Triplet and phosphorescence parameters The various unimolecular processes involving the triplet state include (a) T( - So phosphorescence; (b) T( - So intersystem crossing; (c) S( - T( and S( - Tq intersystem crossing; (d) So - T( and So - Tq absorption; (e) T( - Tq absorption; (f) Tq - T( internal conversion; (g) Tq - T( fluorescence; (h) Tq - S( intersystem crossing; (i) Sp - Tq intersystem crossing; and (j) biphotonic ionization via T(. Process (b) has been discussed in Chapter 5. The remaining unimolecular processes are considered in the present Chapter. Homopolar bimolecular processes involving the triplet state are treated in §7.l8 and Chapter 8. In dilute solution the three processes competing for the (M* excitation energy, and their corresponding rate parameters, are (i) fluorescence (kFM); (ii) S( - T( and S( - Tq intersystem crossing (kTM ); and (iii) S( - So internal conversion (kGM)' The total rate of these processes is kM = kFM

+ kTM + kGM

(6.1)

The two processes competing for the 3M* excitation energy, and their corresponding rate parameters, are (iv) T( - So phosphorescence (k pT ); and (v) T( - So internal quenching (kGT)'

The Triplet State 6.1

194

The total rate of these processes is kT = kpT +kGT

(6.2)

For steady excitation of I M* with a low light intensity of 10 einstein I-I S-I of a dilute solution of molar concentration [iM], the rate equations are

10 - kM[iM*]

(6.3)

k TM [iM*] - kTPM*]

(6.4)

d[IM*] dt d[3M*] dt

=

=

Light of low intensity is specified to exclude bimolecular 3M* - 3M* processes, the rate of which is proportional to PM*]2 (Chapter 8). Under photostationary conditions, d[i M*]/dt = dPM*]/dt = 0, and 10 produces photostationary concentrations [iM*]. and PM*]s of the two excited species. We define the triplet quantum yield py [,pc- tc

(6.30)

(iii) the observed mean phosphorescence intensity [py, averaged over the viewing cycle only, and given by _ 4>py [,py- -

ty

(6.31)

The yield 4>py is a maximum, (4)PY)m, when tx = t L , i.e. when the delayed emission is viewed immediately after the excitation period so that (6.32) The yield (4)py)m is increased by increasing the viewing time tv, and in the limit, when ty ;P 'Tn (4)py)max = 'TT{lP)O, i.e. all the phosphorescence emission is observed. The increase of tv, without change in tc , has no effect on [p, it increases [pc, but it decreases [py. The distinction between [p, [pc and [py is stressed for two reasons. In the first place much of the literature on spectrophosphorimetry is vague or inaccurate on this point. In the second place the mode of detection determines which of the three parameters is observed, and the sensitivity of detection. The phosphorescence is detected with a photomultiplier or other lightsensitive device. The instantaneous photomultiplier current is proportional to [p. The phosphorescence lifetime 'TT is normally measured by the observation of [p as a function of t, using an oscilloscope synchronized to the phosphorimeter chopping frequency.

204

The Triplet State 6.4

measured 15

Phosphorescence spectra are commonly by observing the integrated photomultiplier signal, recorded as a D.C. current, which is proportional to fpc. This method, though simple, does not utilize the broad-band high-frequency characteristics of the photomultiplier. In general (6.33) so that an improved signal-to-noise ratio, resulting in higher sensitivity, can be achieved by observing fpv or fp. The observation of fpv is relatively simple. The phosphorimeter modulates the photomultiplier signal, and a pulse amplifier whose frequency characteristics match those of the phosphorimeter can be used to amplify the signal , thus providing a D.C. output current proportional to f pv . Provided tv ~ TT, a condition which is readily achieved in practice since TT is usually ~l ms or longer, fpv approximates Closely to the instantaneous intensity f p • Few experimentalists appear to have used this method to improve the sensitivity ofspectrophosphorimetry. Similar principles are applicable to the detection of weak luminescence spectra of short duration, e.g. fluorescence and scintillation spectra, although the condition tv ~ TF , the luminescence decay time, cannot be achieved with mechanical choppers. The photon-sampling technique, which is used for the measurement of TM as described in §4.6, can be adapted to spectrometry by scanning the optical spectrum of the emission rather than its time spectrum. 16 This technique has been used to observe the weak luminescence spectra of noble gases excited by individual ionizingparticles. 17 When tx = t L, (CPpV)m from (6.32) is a maximum if tv = to. This pattern of phosphorimeter in which the discs C 1 and C 2 are complementary, so that tL = tN, to = tv, is the opposite to the case considered above, where the discs C 1 and C 2 were identical (tL = tv, to = tN)' Ideally the complementary disc pattern gives the maximum phosphorescence yield (for a given excitation time t L), but the setting of the relative phase Ix to equal tL (and thus eliminate prompt fluorescence) with this disc pattern is too critical in practice, because oflight scattering. The phosphorimeter design is usually a compromise between the complementary and identical disc patterns, with tL < tv < tD' For example, in the phosphorimeter of Parker,14 the total period tc = 1/800 s, and tL = !tc , to = it c , tv = ttc and tN = ttc. The phosphorescence intensities f p, fpc and fpv depend not only on the viewing cycle, but also on the excitation cycle, which determines (/p)Q. In the simplest case, where t D }> TT, there is no residual PM*] from the previous excitation cycle. Under these conditions (6.34)

6.4 SpectrophosphOi'imetry

205

where (/JPT/O is the photostationary phosphorescence intensity under steady excitation by an absorbed light intensity 10 , Hence, from (6.29) and (6.34), (6.35) For tx = tL , from (6.32), (cppv)m =

7'T (/JPT

loCI - e- tL / 7T)(1 - e- tV / 7T)

(6.36)

(CPpv)m attains its maximum possible value ( = 7'T(/JPT / o) when t L l!> 7'T, tv l!> 7'T' This occurs when the discs are rotated sufficiently slowly to enable the maximum phosphorescence intensity, (/JPT/o, corresponding to a photostationary triplet concentration [3M*]s ( = 7'T(/JTM / o) to be achieved, and for the total phosphorescence yield, 7'T(/J PT / o, to be detected. The conditions for maximum Ip, Ipy and Ipc differ from those for maximum (CPpv)m' lp is a maximum, from (6.34), of magnitude (6.37) when tx = tL and tL l!> 7'T' Ipv is a maximum under the same conditions, and it approximates to Ip, provided tv for the aromatic hydrocarbons (Table 5.4) with the observed TI - Tq absorption spectra (Table 6.9) shows the unsatisfactory current situation. In only one compound, anthracene, is LIsT > 11,000 cm- I, and this is the only compound in which a TI - Tq absorption transition to an excited triplet state lying below SI has been detected. In all the other compounds LIsT < 11 ,000 cm- I, so that absorption transitions from TI to any triplet state lying below SI are probably outside the present limits of photoelectric detection. The alternative approach to the observation of triplet states lying between TI and SI is that of So - Tq absorption spectrometry, using one of the methods described in §6.8. The oxygen perturbation technique has been used by Colson and Bernstein35 to observe the So - TI and So - T2 transitions in solid benzene and perdeuterated benzene at 4·2°K. The difficulty of observing the latter transition is that T2 lies only -900 cm- I below SI> and even under O 2 perturbation the intensity of the So - T 2 transition is at least 100 times weaker than that of the So - SI transition. This necessitates the use of low temperatures to eliminate hot bands (§3.2) associated with the latter. The So - T2 absorption bands (but not the weaker So - TI absorption bands) have also been observed directly35 in pure C6H6 and C6D6 crystals, up to 5 cm in length, at 4·2°K. Table 6.12 lists these and other experimental data on transitions involving triplet states in benzene. Kearns 36 has discussed the assignment of the three lowest triplet states observed in benzene, and his assignments are shown in Table 6.12. Godfrey and Porter 37 have observed a broad structureless triplet-triplet band with a possible maximum at -41 ,600 cm- I in benzene in a low-temperature glass by flash photolysis. Recently Astier et al. I09 have observed a TI - Tq band at 23,250 cm- I, assigned by Birks 110 to the TI - T4 transition. Hanson and Robinson 38 have made similar observations of the So - T q absorption spectra of extremely pure naphthalene crystals at 4·2°K. As in benzene, two absorption bands are observed: a very weak transition to TI> barely detectable in a 4 cm thick crystal, and a stronger transition (-10-10 2 times the So - TI absorption intensity) to T 2 , which lies -750 cm- I below SI. TI (=3L. ) has two Davydov components (§11.4) at 21,203 cm- I and 21,213 cm- I, and their centre of gravity is close to the 0 - 0 band at 21 ,209

The Triplet State 6.11

224

em-I observed in the phosphorescence spectrum of naphthalene in naphthalene·d g•39 T2 has two Davydov components at 30,785 em-I and 30,814 em-I, corresponding to a mean energy of 30,800 em-I. SI (= IL b ) has Davydov components at 31,475 em-I and 31,624 em-I, with a mean energy of 31,550 em -I. Bands are observed 30 in the threshold electron impact spectrum of naphthalene at -22,000 em-I, -31,000 em-I and 43,500 em-I. The first two bands are assigned to the TI and T2 states, observed in the So - Tq crystal absorption spectrum. The sharp intense band at 43,500 em-I corresponds to a higher triplet state. The intense band at 24,100 em-I observed in the triplet-triplet absorption spectrum (Table 6.9) corresponds to a further triplet state with an energy of 45,300 em-I. For anthracene (TI = 3La = 14,700 em-I) a triplet state T2 at 25,900 em-I has been observed by flash photolysis. 40 This lies below SI (= ILa = 26,700 em-I) in solution, but above SI (=24,910 em- I) in the crystal. This explains the difference between the fluorescence quantum efficiency of anthracene in solution (10" (6.55)

eEq -

,

'L q> 1

~ 30, -

(3 E

q

-

3E

,

)

Lp

(I E

2 {J" 10"

"

-

3E

I

)

(6.56)

p

The second term in (6.55), which does not change the multiplicity, can be neglected. The magnitude of each {J" 10" term depends inversely on the energy gap (' E" - 3 E I ) and on the symmetry of 10" relative to 30 1, In centrosymmetric molecules, such as the polyacenes, the states are of even (g) or odd (u) parity. Spin-orbit coupling occurs only between states of the same parity. The ground state So (= IA lg) is of even parity, but the lower excited states are of odd parity. In a simple treatment we may neglect spin-orbit coupling to 10 0 , since OC q = 0 except for higher triplet g-states. Spin-orbit coupling to 30, (= 3B 2u ) can occur from those excited singlet states, which are of odd parity and which differ in symmetry from B 2u , namely I B 3u , IB,u and I A,u' Table 6.14 lists the various singlets which can combine with triplets through spin-orbit coupling. This is an extended version of the table given by Pariser. 2o Only the states indicated by an asterisk correspond to 7T-electronic states. ax> a y and a z are the spin-orbit vectors with coordinates x and y corresponding to the long and short molecular axes, respectively, and z to an axis perpendicular to the molecular plane. The T, - So phosphorescence transition probability k pT is proportional to the square of the electric dipole transition moment M PT , where

MPT = ( 30; IMIIOo>

~ (3 0, - ~ {J" 10"IMII00) =

-2 {J"( IO,,IMI'Oo> p

(6.57) (6.58) (6.59)

228

The Triplet State 6.12

The term 210 nm the initial excitation is restricted to 'M* since mono-olefins do not absorb in this region; and 1 M * - 1 y* energy transfer does not therefore occur. The cis- and trans-isomers of butene-2 are convenient, since they are both available in a state of high purity and are easily analysed by gas chromatography. The value of IPTM depends on the cis/trans ratio c/t. For butene-2 Cundall and co-workers obtained c/t = 0·75 ± 0'01,92 and this value forms the basis of the IPTM values reported by Cundall et al. 91 - 93 and Noyes and Harter. 95

6.16 Vapours of Benzene and its Derivatives

243

Sato et al. and Haminger and Lee 96 obtained values of cit ::-: 1·0 and 0·98, respectively, for butene-2 with benzene as the sensitizer. The latter value has been used by Noyes and co-workers97 - 98 to determine or recalculate CM = 0, as observed, and if>UM = 0, showing that the isomerization hypothesis is redundant at "ex ;:;' 250 nm. In benzene at p > 10 torr, reduction of "ex causes a decrease in if>FM to ~O at "ex ';; 240 nm (Table 6.19) and there is evidence 94 for a similar decrease in if>TM (Table 6.20). There is some increase in the photochemical yield if>CM' but this is inadequate to account for the resultant quantum efficiency deficit Llif>. The results thus provide clear evidence for an efficient and rapid process that competes with the collisionally-induced vibrational relaxation. There are three possible candidates for such a process: (a) SI - So internal conversion via an isomer, quantum yield if>UM; (b) self-quenching, quantum yield if>OM; and (c) collisional quenching by a photoproduct X, quantum yield if>xM' Processes (b) and (c) have been discussed in connection with the similar decrease of if>FM with "ex observed in benzene solutions (§5.14). In benzene vapour the decrease of if>FM to zero occurs even at low pressures, where the pressure-dependent processes (b) and (c) are inoperative. It is therefore concluded that the SI - So isomer internal conversion process (a) is primarily responsible for the decrease in if>FM at "ex ';; 240 nm. Foote et al. 105 and Shindo and Lipskyl06 have studied the photochemistry of benzene vapour at "ex = 184·9 nm (S3 = lEI u), where if>FM = O. The photochemical yield if>CM = 0·25, 0·13 and 0·10 at p = I, 2 and 3 torr, respectively, and it extrapolates to if>CM ~ 1·0 at zero pressure. 106 There are two main products, a benzene isomer subsequently identified I07 as fulvene H HC=~

I / C=CH2 HC=C H

6.16 Vapours of Benzene and its Derivatives

247

and an unidentified polymer. These results show the existence of all three processes (a), (b) and (c). Fulvene is a benzene isomer U and also a photoproduct quencher X, and polymerization implies a dimeric intermediate D. The decrease of if>CM with increase of p indicates a competing radiationless process whose quantum yield increases with p, which is consistent with collisionally-induced internal conversion via an isomeric state (if>UM) or self-quenching (if>OM). For Aex > 250 nm and p > 10 torr, thermal equilibrium is established collision ally during the IM* lifetime, so that (if>FM)O corresponds to the fluorescence quantum yield , corrected for self-quenching, of a system of excited molecules with a Boltzmann distribution of energies among the lowest vibrational states of S). For Aex < 240 nm, the S) - So isomer internal conversion process competes with such vibrational relaxation. In the low pressure region (p < 0·5 torr) the mean interval between molecular collisions exceeds the fluorescence lifetime,82 so that thermal equilibrium is not established collisionally. For Aex = 253·7 nm, if>FM is independent of p «0·5 torr),82-84 and resonance fluorescence occurs from the initially excited vibronic state. Parmenter and Schuyler))) have recently studied the fluorescence spectra originating from individual vibronic levels of benzene, excited by light sufficiently monochromatic (~30 cm-) band spread) to preclude excitation of multiple levels, and at p < 0·2 torr to prevent collisional redistribution of the energy prior to fluorescence. These spectra all have a similar appearance and consist of bands whose displacements from the exciting line are common to all the spectra. With excitation into the lower vibrational levels of 1B 2u the spectra are sharp and well-structured, but excitation into higher levels tends to give more diffuse spectra, attributed to intramolecular redistribution of the vibrational energy. The fluorescence quantum yield if>FM drops sharply to zero when vibrational levels of energy greater than E z = 2500 cm- 1 above the zero-point energy are excited, showing the sudden onset of an efficient competing intramolecular radiationless process Z. A similar decrease of if>FM with Aex is observed in benzene, benzene·d 6 and toluene atp > 10 torr (Table 6.19), but the threshold energy E z is much less clearly defined in the presence of collisional vibrational relaxation. The triplet quantum yields if>TM of benzene and toluene at p > 10 torr (Table 6.20) also tend to decrease with Aex> indicating that Z is not an intersystem crossing process. However, the isomerization technique is of doubtful validity for vibrational energies above E z, since it involves introducing a foreign gas which produces collisional vibrational relaxation. Process Z probably corresponds to the spin-allowed crossover to a vibrationally excited level of a benzene isomer lU, resulting from the vibrational distortion of the benzene ring, as proposed by Lamola et al. 104 Atp > 10 torr, or in

248

The Triplet State 6.17

solution in a condensed medium, rapid vibrational relaxation of IU will occur, leading to crossover from IU to IM and a small photochemical yield oflU. This radiationless isomerization process provides an efficient mechanism of SI - So internal conversion, which differs from that considered in §5.11. It accounts satisfactorily for the large magnitude of the frequency factor k;M = 1·2 x 10 12 S-I of the temperature-dependent internal quenching rate of benzene in hexane solution (Table 5.2), which is characteristic of a spin-allowed process. The activation energy WIM = 0·35 eV of the internal quenching agrees closely with that of E z = 2500 cm- I = 0·32 eV. The data on toluene in the vapour phase (Tables 6.19 and 6.20) and in solution (Table 5.2) indicate that it behaves in a similar manner to benzene. For benzene atp < 0·5 torr, ;\ex = 253'7 nm (i.e. vibrational energy < E z ), the values of FM = 0'39, GM = 0-0'05, OM = 0, CM = 0, show that TM + UM ;;;' 0·56. Although there are no reliable data on TM at low p, the values at p > 10 torr (Table 6.20) indicate that intersystem crossing to the triplet manifold is the main radiationless process competing with the fluorescence (i.e. UM ~ 0). The theory of radiationless transitions in molecules in solution treats the environment as an efficient vibrational energy sink, so that the transition is irreversible (§5.6). An isolated molecule must act as its own energy sink. The density of vibrational states in the triplet manifold, which are quasi-degenerate with the initial singlet vibronic state, is relatively high, and intramolecular redistribution of the vibrational energy between these states probably inhibits the reverse T - SI intersystem crossing process. Robinson 77 • 85 and Bixon and 10rtner lo8 have recently discussed radiationless transitions in isolated molecules (see p. 628). 6.17 The triplet state of benzene

The triplet state T I (= 3Btu) of benzene has several unusual properties. Unlike higher aromatic hydrocarbons, the triplet lifetime 'TT of benzene and benzene·d 6 in rigid glass solution increases appreciably in cooling from 77° to 4°K. For benzene 'TT = 7 s at 77°K, and 16 s at 4°K. This has been explained by de Groot and van der Waals l12 in terms of a lahn-Teller distortion of triplet benzene, which leads to a low-frequency mode, corresponding to the interchange between two differently distorted regular hexagons. Thermal excitation of this mode increases the Franck-Condon factor for the radiationless Tl - So transition. This model is analogous to the isomer hypothesis introduced to account for the thermally-activated Sl - So internal conversion (§6.16). Hatch et al. 122 have studied the temperature dependence of kT (=I/'TT) for benzene and deuterated benzenes in various rigid glass solutions. They

6.17 The Triplet State of Benzene

249

analysed the results in terms of an Arrhenius relation, analogous to (6.63) kT = kPT + kg T + kC:JTexp(-WGT/kT)

(6.86)

which gives a good fit (standard deviation -5 %) to the data. The values of k~T and W GT , listed in Table 6.21, are dependent both on the nature of the solute and of the solvent. The replacement of a hydrogen atom in benzene by a deuterium atom results in a -33 cm- ' increase in the S, - So and T, - To 0 - 0 transition energies, so that ET (C6D6) - ET (C6H6) ~ 200 cm-' (Table 6.12). Martin and Kalantar''3 have made a detailed study of the phosphorescence lifetime TT of most of the deuterobenzenes in rigid 10- 3 M solutions in 3-methylpentane, isopropanol and cyclohexane at 77°K. With increasing deuterium substitution TT increases in the same order in all three solvents. The values for some of the compounds are listed in Table 6.22. To obtain values of TT, reproducible to within ±1 %, the 3-methylpentane solutions were allowed to relax for 3 hours at 77°K during which time TT increased to a steady value, the cyclohexane solutions were annealed into the monoclinic phase at I80 K for a half-hour, while the isopropanol solutions were cooled rapidly. Expressing 0

(6.2) and taking kPT = 0·034 s-, as constant, independent of deuteration, the changes in TT are attributed to changes in kGT' the rate of T, - So intersystem crossing. Table 6.23 lists the values of kGTo and the change LlkGT/H in kGT per hydrogen atom replaced by deuterium. LlkGT is largest in going from C6D6 to C6HDs. For the intermediate compounds it is found that TT decreases in the order 1l4 : C6 D 6 ~ C6DSH > m-C6D4H2 > sym-C6D3H3 > p-C6D4H2 > asym-C6D 3H3 > vic-C6D2H4 > p-C6H 4 H 2 - o-C6H4D2 > C6 H SD > C6 H 6 These results provide clear evidence that CH modes contribute strongly to kGT (§5.9). The order of the TT values indicates that adjacent (ortho) CH groups contribute more to kGT than do opposite (para) CH groups, and that meta CH groups contribute less than either. Nieman 1l7 has made a detailed vibrational analysis of the phosphorescence spectra of the deuterobenzenes. The CH- and CD-stretching vibrational spectra of the compounds were studied in the near infra-red to see if the differences in TT for equally deuterated benzenes could be related to differences in anharmonicity among

250

The Triplet State 6.17 114

the CH-stretching modes. The similarity of the combination-overtone spectra provided no evidence linking anharmonicity and Tl - So intersystem crossing (§5.9). Hirayama 115 has observed the concentration dependence of WPT/WFM and 'TT for benzene solutions in EPA, p-dioxan and cyclohexane at 77°K. In the EPA solutions WPT/WFM and 'TT decrease together at [1M] > 0·01 M, approaching zero at [1M] - 1 M. This behaviour is consistent with triplettriplet migration, leading to increased triplet quenching. In the dioxan solutions WPT/WFM decreases to zero at -0·5 M, while 'TT remains constant up to 1 M, which is consistent with increasing aggregation of the benzene molecules into non-phosphorescent microcrystals. The behaviour of the cyclohexane solutions is unusual, in that WPT/WFM is practically constant up to 1 M and then decreases to zero at 2 M, while 'TT increases by a factor of 2 between 0·1 and 0·7 M. Hirayama 115 suggests that this is related to the cubic and monoclinic structures of mixed benzene-cyclohexane crystals. These results illustrate the complex influence both of concentration and solvent environment on the behaviour of the benzene triplet state (see p.629).

The Triplet State

251

Table 6.1 Quantum yields of triplet formation (lPTM ) and fluorescence (lP FM ) (in dilute solution at room temperature, unless otherwise stated) see also Table 12_1, p_ 637 Code

Compound

2

Naphthalene

2d

Naphthalene-d 8

2A

I-Methylnaphthalene

2B

2P 2X

2Z

3_1

cJ>TM

Ref_

cJ>FM

Ref_

cJ>TM

+ cJ>FM

Benzene Benzene Ethanol Ethanol Benzene Cellulose acetate (77°K) Benzene

0-40 0-82 0-80 0-71 0-38 0-53

a b b c a d

0-28 0-28 0-21 0-21 0-28 0-47

b b b c b d

0-68 1-10 1-01 0-92 0-66 0-00)

0-48

a

e

0-69

2-Methylnaphthalene

Benzene

0-51

a

0-21 (in cyclohexane) 0-27 (in cyclohexane)

e

0-78

I-Fluoronaphthalene I-Methoxynaphthalene

Benzene

0-63

a

Benzene

0-26

b

0·79

Ethanol Ethanol Benzene

0-50 0-46 0-47

b c e

1-03 0-99 0-97

Ethanol Ethanol Ethanol Ethanol Liq_ paraffin Liq_ paraffin EPA (77°K) Liq_ paraffin Ethanol Ethanol

0-58 0-45 0-72 0-70 0-58 0-75 0-53 0-48 0-67 0-03

0-53 (in ethanol) 0-53 b 0-53 c 0-50 a (in cyclohexane) 0-39 b c 0-39 0-30 b 0-30 c, h 0-33 i f, g 0-31 j g 0-51 0-33 c 0-89 c

b c b c, h i f, g

0-97 0-84 1-02 1-00 0-91 1-06

g c c

0-99 1-00 0-92

Liq_ paraffin Ethanol Liq_ paraffin Liq_ paraffin Isopropanol Ethanol Ethanol Ethylene glycol Liq _paraffin

0-12 0-02 0-37 0-35 0-51 0-47 0-51 0-24 0-43

f, g c f g f c I I g

0-81 0-89 0-57 0-57 0-46 0-49 0-45 0-68 0-52

f, g c f g f c I I g

0-93 0-91 0-94 0-92 0-97 0-96 0-96 0-92 0-95

Ethanol

0-48

k

0-56

k

1-04

Acenaphthene

Anthracene

3.1d Anthracene-d lO 3_1A 9-Methylanthracene 3.1B 9,1O-Dimethylanthracene 3.1C 9, 1O-Diphenylanthracene 3_1D 9-Phenylanthracene

9-Ethylanthracene 3.lH 9,IO-Dichloroanthracene 3.lE

Solvent

a

The Triplet State

252 Table 6.1 (continued) Code

Compound

3.2

Phenanthrene

3.2d

Phenanthrene·d lO

4.1

Pyrene

4.2

Tetracene

4.3

1 :2-Benzanthracene

4.4

Chrysene

Solvent Benzene Ethanol Ethanol 3-Methylpentane Cellulose acetate (77°K) Cellulose acetate (77°K) Cellulose acetate (77°K) Ethanol Ethanol Ethanol Propylene glycol (1800 K) Benzene Hexane Hexane Ethanol Polymethylmethacrylate EPA (77°K) Benzene Ethanol Ethanol EPA (77°K)

+

203 217-8

~

i: II>

-00

= II>

3-Methylpentane (77°K)

4.1

Pyrene

Liq. paraffin (20°C)

Pyrene·d lO

4.2

Tetracene

...~

i:

192·5 (0'24) 207 (0,19)

Vapour (100°C) EPA (77°K)

4.1d

~

192·2

Hexane (20°C)

Epoxy resin (25°C)

~

121·3 137·5 153-8 168·3

190·5 (0'20) 194 204·5 (0,15)

1: 2-Benzanthracene

2-MethyItetrahydrofuran (77°K) Liq. paraffin (20°C)

210 (0,16)

Hexane (20°C) Liq. paraffin (20°C)

c

240·5 (1'00) 254 (0'55) 217·4 (0,27) 232·3 (0'14) 250 (0,04) 236·3 249·9

m

--~

00 ~

~

d h f

115 129

Vapour (160°C) 4.3

243·3 258·3 271 240·4 (1'00) 252·2 (0,48) 269·1 (0,26) 253·5 240·7 (1·00) 269 (0,10)

185·2 (0'12)

206·2 222·2 232·6 206·2 (1·00) 216·9 (0'84) 230·1 (0,53) 241 (0'38)

319 (0,04)

350·3 (1 '00)

d h

c 317'5

d N

-..I ~

N

Table 6.9 (continued) Code

4.3

Compound

1:2 Benzanthracene

Solvent

EPA (77°K) EPA (77 OK)

isopentane/methylcyclohexane (77°K) Polymethyl methacrylate (23°C) Vapour (200°C) Hexane (20°C)

4.4

Chrysene

Hexane (20°C) EPA (77°K)

1

-.,J

'"

2

204·5 211·3 217·7 204·5 (1'00) 211 217 (0'58) 230·5 (0,54) 205·5 (1'00) 212 218 (0'62) 232·5 (0·55) 206 (1,00) 218 (0'72) 231 (0'62) >217'4, wide band, max. at 221·1 208 219 219 232 175-4 (1·00) 171·2

3

4

5

Ref.

e f

f

n h 279

249-4 (0,20) 264·6 (0'17)

338 357 357

0

=""' ~

~

-

d

'£ ~

e

S'

'JJ ~

159 (0,11) 171·5 (1-00) 177-5 185

EPA (77°K)

0

4.5 4.6

3: 4-Benzophenanthrene Triphenylene

Epoxy resin (25°C) 110 2-Methyltetrahydro[uran (77°K) Hexane (20°C)

5.1 5.3

Perylene 3: 4-Benzopyrene

3-Methylpentane (77°K) Hexane (20°C) EPA (77°K)

5.4

Pentacene

Hexane (20°C)

5.6

1: 2: 3: 4-Dibenzanthracene

2-Methyltetrahydro[uran (77°K)

[

(!>

.... (!>

239 (0,14)

m

r./l

S" .... (!>

250 (0'33)

d

289 (1'00)

d e g h I

357

204·9 198·5 (0·31) 209·5 (0,95) 213-7 (1'00) 225 (0,76) 204 (0'33) 218·8 (0'17) 220·5 (1·00) 234 (0'50) 247 (0'33)

=-

:;l

137·5 151 ·3 138·8 152·3

190 (0,05)

I-l

§:

233 ·6 (0,65) 247·5 (0'50) 232 232 (1'00) 245 (0'56) > 244

Hexane (20°C) EPA (77°K) Butane/ isopentane (77°K) Vapour (200°C) EPA (77°K)

171 (1 '00) 182 (0'39) 193-4 (1·00)

246·3 (0'18) 260 (0'15)

d [

260 (0'1)

327·9 (l·00)

d

m ~

UI

Table 6.9 (continued)

Code

Compound

1

Solvent

2

3

187-8 (1·00) 200·4 (0·86) 213 (0·70) 171 183 197·5 202 171 (1·00) 182·8 (0·67) 197 (0·39) 200 (0·40) 212 (0·30) 170·5 (1·00) 181 (0·67) 197 (0·38) 210 (0·30) 228 (0·22)

235·8 (0·50) 251·3 (0·27) 265·4 (0·14)

4

5

Ref. ~ Q\

5.7

1 :2:5:6-Dibenzanthracene

Hexane (20°C) EPA (77°K)

EPA (7TK)

2-Methyltetrahydrofuran (77°K)

5.9

7.1

Picene

Epoxy resin (25°)

Coronene

2-Methy Itetrahydrofuran (77°K) Hexane (20°C)

d e

233·5 (0·24)

f

m

110 124·2 157·3

m 158·8

Hexane (20°C) EPA (77°K) 2-Methy ltetrahydrofuran (77°K) Epoxy resin (20°C)

306

204 216·5 190·6 (0.33) 208·3 (0·68) 216·90·00)

c

206·5

m

206

q

d

1-3

=-

. ("I>

1-3

--

~ ("I>

158

rFl ~

90 95 102

113·5

156 169 180

("I>

EPA (77°K) 8.4

A

1 : 2-Benzocoronene

Biphenyl

157 170 183 176 (0-89)

Po]ymethylmethacrylate (23°C) EPA (77°K) Liq_ paraffin (20°C) Butanol (77°K)

B

Fluorene

- 250

Liq_ paraffin (20°C) Liq_ paraffin (20°C) Vapour (95°C) /sopentane/methylcyclohexane (77°K) EPA (77°K)

D

p- Terphenyl

2-Methyltetrahydrofuran (77°K) Butanol (77°K)

E

p-Quaterphenyl

Butanol (77°K)

H

Rubrene

Hexane (20°C)

J L

m-Terphenyl o-Terphenyl

Butanol (77°K) Butanol (77°K)

238 198-8 (0-22) 204-1 237-5 (0-23)

168 (0-56) 174-5 (0-68) 185 (0-41) 271-3 (1-00) 284-1 (0-69) 268 275 281 261 261-5 (1-00) > 263 max_ at 284, 302 253 258 (1-00)

207

252 261

q

240 (1 -00)

n

237 (1-00)

n

;;l n>

.,1-3

~ n>

--= rJ'J

d

n>

p c d h f

199 (due to photoproduct) -240 (0-11) 218 223 191 202 186 (0-58) 192-7 (1-00)

191 203 Table references are given on p_ 278_

260-5 (1-00)

m P

p 238-9 (0-25)

d

250

p P

N

-..I -..I

278

The Triplet State

References

a. R . Astier, A. Bokozba and Y. H. Meyer, Transitions Non Radiatives dans les Molecules, Paris, 1969;J. Chim. Phys. (in press). R. Astier and Y. H. Meyer, Chem. Phys. Lett., 3, 399 (1969). b. T. S. Godfrey and G. Porter, Trans . Faraday Soc., 62, 7 (1966). c. G. Porter and M. W. Windsor, Molecular Spectroscopy, p. 6, Institute of Petroleum Conference, 1955. d. G. Porter and M. W. Windsor, Proc. Roy. Soc. A, 245, 238 (1958). e. D. S. McClure, J. Chem. Phys., 19, 670 (1951). f. D. P. Craig and I. G. Ross, J. Chem. Soc., p. 1589 (1954). g. R. A. Keller and S. G. Hadley, J. Chem. Phys., 42, 2382 (1965). h. G . Porter and F. J. Wright, Trans. Faraday Soc., 51, 1205 (1955). i. R. E. Kellogg, J. Chem. Phys., 44, 411 (1966). j . M. W. Windsor and J. R. Novak, The Triplet State, p. 229, Cambridge University Press, 1967. k. R. Astier and Y. H. Meyer, The Triplet State, p. 447, Cambridge University Press, 1967. I. B. R. Henry and M. Kasha, J. Chem. Phys., 47,3319 (1967). m. J. S. Brinen, J. Chem. Phys., 49, 586 (1968). n. W. R . Dawson, J. Opt. Soc. Am., 58, 222 (1968). o. H. Labhart, Helv. Chim. Acta, 47, 2279 (1964). p. I. A. Ramsay and I. H. Munro, The Triplet State, p. 415, Cambridge University Press, 1967. q. M. W. Windsor and J. R. Novak, Molecular Luminescence, p. 365 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. r. W. H. Melhuish, J. Chem. Phys. 50, 2779 (1969).

279

The Triplet State Table 6.10 Effect of photoselection on measured triplet-triplet extinction coefficient (€TT)m

Exciting light

UE.UT

EE. ET

Polarized Polarized Polarized Polarized Polarized Polarized Non-polarized Non-polarized

1 0 1 0

1 0 0

0 1 0

IT IT IT IT

non-polarized non-polarized non-polarized non-polarized

(€TT)m/€TT

9/5 3/5 3/5 6/5 6/5 9/lD 6/5 9/10

280

The Triplet State Table 6.11 Maximum triplet-triplet molar extinction coefficients

Code 2

Compound Naphthalene

2d

Naphthalene·d B

3.1

Anthracene

3.ld

Anthracene·d lo

3.2

Phenanthrene

3.2d

Phenanthrene·d I 0

4.ld

Pyrene·d 1O

4.2

Tetracene

4.3

1:2-Benzanthracene

4.4

Chrysene

Solvent Liq. paraffin (20°C) EPA (77°K) Butane/isopentane (77 OK) Cyclohexane (20°C) Ethanol/methanol (l13 °K) 3-Methylpentane (77°K) Liq. paraffin (20°C) EPA (77°K) Cyclohexane (20°C) Ethanol/methanol (113°K) EPA (77°K) Ether /ethanol/ toluene (77°K) Butane/isopentane (77°K) 3-Methylpentane (77 OK) Cyclohexane (20°C) 3-Methylpentane (77 OK) 2-Methyltetrahydrofuran (7rK) Liq. paraffin (20°C) Liq. paraffin (20°C) 2-Methyltetrahydrofuran (77°K) Cyclohexane (20°C) EPA (77°K) Hexane (20°C) Hexane (20°C) 2-Methyltetrahydrofuran (77°K)

jj

(10 2 cm- I )

(ETTmax)

E'TTmax

Ref.

241

10000

a

240 241

> 10000 14000

b c

242·5 242

22600 45000

d e

241 242 235·8

31900 23300 71500

f, g k a

234·2 238 235·1

>45000 57200 90000

b d e

235·3

115000 75000

h f

203

27000

c

204·1

41500

f, g

207-3 204·7 205·4 240·5

21000 42900 20400 43600

d f, g k f

217·4 319 350·3 185·2 206·2 203

52600 8000 195000 3000 23400 43600

208·3 203 208 175·4 249·4 171

25100 29000 18000 8800 1800 48600

a a f d j

a f

The Triplet State

281 Table 6.11 (continued)

Code 4.5 4.6

Compound 3 :4-Benzophenanthrene Triphenylene

5.4

Pentacene

5.6

1 :2: 3 :4-Dibenzanthracene

5.7

1 :2:5:6-Dibenzanthracene

5.9

Picene

7.1

Coronene

8.4

1 : 2-Benzocoronene

A

Biphenyl

B

Fluorene

N

Benzophenone Biacetyl Acridine

Solvent Hexane (20°C) Hexane (20°C) EPA (77°K) 2-Methyltetrahydrofuran (77°K) Hexane (20°C) 2-Methyl tetrahydrofuran (77 OK) 2-Methyltetrahydrofuran (77°K) Hexane (20°C) 2-Methyltetrahydrofuran (77°K) Hexane (20°C) 2-Methyltetrahydrofuran (77°K) EPA (77°K) 2-Methyltetrahydrofuran (77°K) EPA (77°K) Benzene (20°C) 2-Methyltetrahydrofuran (77°K) Benzene (20°C) Cyclohexane (20°C) Cyclohexane (20°C)

jj

(10 2 cm-I)

ETTmax

Ref.

193'4 250 233 '6 289 232 232 232·6

4800 1580 4100 7000 7000 16500 16800

204 327·9 220·5

205000 630000 31000

f

170·5

25000

f

187-8 235·8 157-3

67000 33400 75500

a f

216·5 206·5

1000 15800

a f

207 170 236·5

15500 25500 38800

I f

175 237 277

26000 38000 35400

d

260·5

20700

f

188

10300

d

317·7

6400

d

231·3

28800

d

a a c f, g k a

282

The Triplet State

References a. G. Porter and M. W. Windsor, Proc. Roy. Soc. A, 245, 238 (1958). b. D. P. Craig and I. G. Ross, J. Chern. Soc., p. 1589 (1954). c. R. A. Keller and S. G. Hadley, J. Chern. Phys., 42, 2382 (1965). d. E. J. Land, Proc. Roy. Soc. A, 305, 457 (1968). e. R. Astier and Y. H. Meyer, The Triplet State, p. 447, Cambridge University Press, 1967. f. J. S. Brinen, J. Chern. Phys., 49, 586 (1968); Molecular Luminescence, p. 333 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. g. S. G. Hadley and R. A. Keller, unpublished data quoted in ref. f. h. M. W. Windsor and J. R. Novak, The Triplet State, p. 229, Cambridge University Press, 1967. i. W. R. Dawson, J. Opt. Soc. Amer., 58, 222 (1968). j. H. Labhart, Helv. Chim. Acta, 47, 2279 (1964). k. D. Lavalette, C.R. Acad. Sci. Paris, B266, 279 (1968). I. M. W. Windsor and J. R . Novak, Molecular Luminescence, p. 365 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969.

The Triplet State

283 Table 6.12 Triplet transitions in benzene (energies in em-I)

Transition T, - So So -T,

Assignment

A,. IA,. I

-

3E,.

Vapour (threshold electron impact) Crystal,4·2°K (absorption) 02-perturbed solid, 4'2°K (absorption) NO-perturbed solid 4'2°K (absorption) Vapour (threshold electron impact) Crystal solution, 4°K (absorption) Vapour (threshold electron impact) Alkane solution 103°K (flash photolysis) !sopentane/3-methylpentane solution, 77°K (flash photolysis)

C6 H 6 29657 29674 30581 31446 32258 29440 30355 31250 -29200 (onset) -31700 (peak) 36947 37496 36560 37170 36983 37324 -36000 (onset) -38000 (peak) 37855

C6D 6

Ref.

29855

a, b

29851 30628 31446 32362

c

d e 37147

c

36784 37495

c f e a

-44000 23250 (T. = 52900) -41600 (peak) (Ts ~ 71300)

e 23250 (T. = 53100)

h g

References

a. b. c. d. e.

G. C. Nieman, Ph.D. thesis, California Institute of Technology (1965). G. C. Nieman and G. W. Robinson, J. Chern. Phys., 39,1298 (1963). S. D. Colson and E. R. Bernstein, J. Chern. Phys., 43, 2661 (1965). D . F . Evans, J. Chern. Soc., p. 1351 (1957). R . N. Compton, R. H. Huebner, P. W. Reinhardt and L. G. Christophorou, J. Chern. Phys., 48, 901 (1968). f. E. R. Bernstein and S. D. Colson, J. Chern. Phys., 45,3873 (1966). g. T. S. Godfrey and G. Porter, Trans. Faraday Soc., 62, 7 (1966). h. R. Astier, A. Bokozba and Y. H . Meyer, Transitions Non Radiatives dans les Molicules, Paris, 1969;J. Chirn. Phys. (in press). R . Astier and Y. H. Meyer, Chern. Phys. Lett., 3, 399 (1969).

The Triplet State 2 I Table 6.13 Energies (10 cm- ) of excited triplet states of naphthalene and anthracene (P, phosphorescence; S, So - Tq absorption; E, threshold electron impact spectrum; T, T I - T q absorption; A, So - Sp absorption; R, experimental value taken as reference energy)

284

Naphthalene

Anthracene

, - - - _ _ _ _ _- - - - . . . J .

Theoretical State TI T2 T3 T4 Ts T6 T7 T8 T9

3Biu 3Bju 3BT; 3BJu 3ATa 3Biu 3BTg 3Etll 3A1a

SI S2

IBJu IBiu

Expt.

212 (P, S) 308 (S)

¥M

(ns)

kFM

(10 6 S- I)

2'1 2·4 7·1 2·0 154 2·0

0·53 164

3·0 5·0

11-6 73

0·66 (20°C) 0'53 0·88

55 5·8

k¥M

(10 6 S- I) < 13-3 5·4

8'12

Ig

-

IBA

2

Naphthalene

3.1

Anthracene

5·05

7·38

2·33

4.1

Pyrene

5·35

7·55

2·20

4.2

Tetracene

4·5

6·88

2·38

5.1

Perylene

4·5

7·03

2·53

5.3

3 :4-Benzopyrene

4·9

7·2

2-3

(See also Table 9.5)

10 0·23 254 30 5·2 253·7 0·26 3·0 253'7 0·28 1·2 253 ·7 0·33 4·2 0·23 252 2·0 0·25 252 1·0 252 0·26 10 240 0 10 234·5 0 253 ·7 0·53 0·01-0·4 1,4-d2 -Benzene 0'01-0-4 253·7 0·38 Toluene 24 16- 20 268 0·25 266·8 0·30 0·29 263 256·5 0·24 253·5 0·23 252·2 0·19 250·5 0·17 0·09 248 246·5 0·07 0·005 244 o-Xylene -25 > 10 254 0·35 m-Xylene -25 >10 254 0·25 p-Xylene -25 >10 254 0·40 -25 > 10 254 0·18 Fluorobenzene 0·1 o-Difluorobenzene -25 > 10 254 p-Difluorobenzene -25 > 10 0·25 254 Hexafluorobenzene - 25 > 10 254 0·0015

Benzene

1d

p

29

> 10

( 10 > 10 > 10 > 10 28 19 24 22 18 10 10 10 > 10 > 10 > 10 > 10 > 10 > 10

253·7 253·7 264-9 256-62 249-53 242-52 253·5 253·7 253 ·7 253·7 253·7 266·8 266·8 252 248 248 253 ·7 253·7 253·7 253·7 253·7 253·7 253·7 253·7 253·7

0·63 (0,62) 0·68 0·60 0·58 0·56 0·86 0·55

(0,72) 0·71 (0,78) (0·69) (0,66) (0'64) (0,98) (0·63) 0·61 (0,66) 0·64 0·72 0·65 0·53 0·38 0·32 0·56 0·40 0·67 (0,80) 0·80 0·15 0·53 0·51 (0,05)

91,92 99 94

25

Id lA

Benzene·d 6 Toluene

20 25 24

IB lC ID

o-Xylene m-Xylene p-Xylene Fluorobenzene

25 25 25 25

0- Difluoro benzene

25 25 25 25

m-Difluorobenzene p-Difluorobenzene Hexafluorobenzene

,------'-------,

(0'53)

0·58 (0,55) (0·63) (0,57) (0'46) (0,33) (0,28) (0,49) (0,35) (0,59) 0·70 (0,70) (0'13) (0'46) (0,45) 0·04

92 99 93 99 97

99 99 99 93 99 99 99 99 93

294

The Triplet State

Table 6.21 Temperature and solvent effects on T 1 rate (k GT ) in benzene l22

-

So intersystem crossing

Solvent C 6 H12 - S

WGT

Solute

k'GT (S- I)

(em- I)

C 6H 6 C 6 H SD C 6 HD S C 6D 6

4·6 x 10 3 6·3 x 103 1·8 x 10 4 9·8 X 10 3

570 560 720 790

6·7

1·0

l'6x10 4

860

X

10 3

10 4

480

670

6·8 2·4 1·4 2·0

X

X X X

10 4 10 4 105 105

1000 970 1280 1400

C 6 D12 - M

C 6 D12 - S C 6D 6

X

5·6

X

10 3

640

Solvents: C6 H12 - S, stable (monoclinic) phase of cyclohexane. C6 H 12 - M, metastable (cubic) phase of cyclohexane. B3N3H6' borazine. C 6D 12 • perdeuterated cyclohexane.

The Triplet State

295

Table 6.22 Phosphorescence lifetime 'TT (s) of deuterobenzenes at 77°K in various solvents 113

Compound

3-Methylpentane

Isopropanol

Cyclohexane

C6 H 6 q 3H6

5·75

7-48

4·75

5·68

7·53

4·75

C 6 H SD

6·05

7·95

5·15

C 6 HD s

8·90

10·80

9·50

12·02

13-69

14·10

C 6D 6

The Triplet State

296

Table 6.23 Effect of deuterium substitution on TI - So intersystem crossing rate kGT (10- 3 S- I) in benzene 1l3 Solvent 3-Methylpentane Compound C6 H 6

kGT

kGT/H

140

Isopropanol kGT

100

131

C 6 HD S

78

C 6D 6

49

kGT

92 -13

-16 160 -22

-9 71

58 -29

-19 39

kGT/H

176 -8

-9 C 6 HsD

kGT /H

Cyclohexane

-34 37

6.18 References

297

6.18 References 1. P. G. Bowers and G. Porter, Proc. Roy. Soc. A, 299, 348 (1967). 2. T. Medinger and F. Wilkinson, Trans. Faraday Soc., 61, 620 (1965). 3. A. R. Horrocks, A. Kearvell, K. Tickle and F. Wilkinson, Trans. Faraday Soc., 62, 3393 (1966). 4. A. R. Horrocks, T. Medinger and F. Wilkinson, Photochem. Photobiol., 6, 21 (1967). 5. A. A. Lamola and G. S. Hammond, J. Chem. Phys., 43, 2129 (1965). 6. B. Stevens and B. E. Algar, Chem. Phys. Lett., 1, 58 (1967). 7. B. Stevens and B. E. Algar, Chem. Phys. Lett., 1,219 (1967). 8. C. A. Parker and T. A. Joyce, Chem. Comm., pp. 108,234 (1966). 9. I. V. Aleksandrov and K. K. Pukhov, Opt. Spectrosc., 17, 513 (1964). 10. J. S. Brinen, J. Chem. Phys., 49, 586 (1968); Molecular Luminescence, p. 333 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. 11. H. Labhart, Helv. Chim. Acta, 47, 2279 (1964). 12. R. A. Keller and S. G. Hadley, J. Chem. Phys., 42, 2382 (1965). 13. R. E. Kellogg and R. G. Bennett, J. Chem. Phys., 41, 3042 (1964). 14. C. A. Parker and C. G. Hatchard, J. Phys. Chem., 66, 2506 (1962). 15. c. A. Parker, Photoluminescence of Solutions, Elsevier Publishing Co., Amsterdam, 1968. 16. G. Pfeffer, H. Lami, G. Laustriat and A. Coche, C.R. Acad. Sci. Paris, 254, 1065 (1962). 17. R. Henck, Thesis, University of Strasbourg (1967). 18. C. A. Parker and C. G. Hatchard, Trans. Faraday Soc., 57, 1894 (1961). 19. A. P. Marchetti and D. R. Kearns, J. Am. Chem. Soc., 89, 768 (1967). 20. R. Pariser, J. Chem. Phys., 24, 250 (1956). 21. R. M. Hochstrasser, Behavior of Electrons in Atoms, p. 103, W. A. Benjamin, Inc., New York, 1964. 22. D. S. McClure, J. Chem. Phys., 17,905 (1949). 23. V. L. Ermolaev and K. K. Svitashev, Opt. Spectrosc., 7,399 (1959). 23a. S. R. La Paglia, J. Mol. Spectrosc., 7, 427 (1961). 24. M. Kasha, J. Chem. Phys., 20, 71 (1952). 25. S. P. McGlynn, M. J. Reynolds, G. W. Daigre and N. D. Christodoyleas, J. Phys. Chem., 66, 2499 (1962). 26. D. F. Evans, J. Chem. Soc., p. 1351 (1957). 27. S. P. McGlynn, T. Azumi and M. Kasha, J. Chem. Phys., 40, 507 (1964). 28. G. W. Robinson, J. Mol. Spectrosc., 6, 58 (1961). 29. P. Avakian and E. Abramson, J. Chem. Phys., 43, 821 (1965). 30. J. B. Birks, L. G. Christophorou and R. H. Huebner, Nature, 217, 809 (1968). 31. R. N. Compton, R. H. Huebner, P. W. Reinhardt and L. G. Christophorou, J. Chem. Phys., 48, 901 (1968). 32. D . S. McClure, J. Chem. Phys., 19, 670 (1951). 33. D. P. Craig and 1. G. Ross, J. Chem. Soc., p. 1589 (1954). 34. G. Porter and M. W. Windsor, Molecular Spectroscopy, p. 6, Institute of Petroleum Conference, 1955; Proc. Roy. Soc. A, 245, 238 (1958). 35. S. D. Colson and E. R. Bernstein, J. Chem. Phys., 43, 2661 (1965). 36. D. R. Kearns, J. Chem. Phys., 36, 1608 (1962). 37. T. S. Godfrey and G. Porter, Trans. Faraday Soc., 62, 7 (1966). 38. D. M. Hanson and G . W. Robinson, J. Chem. Phys., 43, 4174 (1965).

298

The Triplet State 6.18

M. A. El-Sayed, M. T. Wauk and G. W. Robinson, Mol. Phys., 5, 205 (1962). R. E . Kellogg, J. Chem. Phys., 44, 411 (1966). M. A. El-Sayed and T. Pavlopoulos, J. Chem. Phys., 39, 834 (1963). R . M. Hochstrasser and S. K. Lower, J. Chem. Phys., 40, 1041 (1964). R. M. Hochstrasser and A. P. Marchetti, Chem. Phys. Lett., 1, 597 (1968). R. L. de Groot and G. J. Hoytink, J. Chem. Phys., 46, 4523 (1967). R. Astier and Y. H. Meyer, The Triplet State, p. 447, Cambridge University Press, 1967. 46. D. S. McClure, J. Chem. Phys., 20, 682 (1952). 47. H. F. Hameka, The Triplet State, p. 1, Cambridge University Press, 1967. 48. V. G . Krishna and L. Goodman, J. Chem. Phys., 37, 912 (1962) . 49. M. A. El-Sayed, Nature, 197,481 (1963). 50. R. A. Keller, Chem. Phys. Lett., 3, 27 (1969); Molecular Luminescence, p. 453 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. 51. H. Schtiler and G. Arnold, Z. Natur/orsch., 16a, 1091 (1961). 52. G. J. Hoytink and K. H. J. Buschow, J. Chem. Phys., 40, 2501 (1964). 53. L. M. Stephenson, D. G. Whitten, G. F. Vesley and G. S. Hammond, J. Am. Chem. Soc., 88, 3665 (1967). 54. P. F. Jones and S. Siegel, Chem. Phys. Lett., 2, 486 (1968). 55. A. R. Horrocks and F. Wilkinson, Proc. Roy. Soc. A, 306, 257 (1968). 56. S. P. McGlynn, T. Azumi and M. Kinoshita, Molecular Spectroscopy o/the Triplet State, Prentice-Hall, Englewood Cliffs, N.J., 1969. 57. A. M. Trozzolo and W. A. Gibbons, J. Am. Chem. Soc., 89, 239 (1967). 58. G. L. Cross, C. A. Hutchinson, Jr. and B. Kohler, J. Chem. Phys., 44, 413 (1966). 59. W. R . Ware and P. J. Sullivan, J. Chem. Phys., 49, 1445 (1968). 60. J. Joussot-Dubien and R. Lesclaux, The Triplet State, p. 197, Cambridge University Press, 1967. 61. J. P. Ray and T. D. S. Hamilton, Nature, 206, 1040 (1965). 62. J. Joussot-Dubien and R. Lesclaux, C.R. Acad. Sci. Paris, 258, 4260 (1964); R. Lesclaux and J. Joussot-Dubien, C.R. Acad. Sci. Paris, 263, CII77 (1966). 63. Kh. Bagdasaryan, Z. A. Sinitsyna and V. Muromtsev, Dokl. Akad. Nauk SSSR, 153, 374 (1963). 64. V. Kholmogorov, V. Baranov and A. N. Terenin, Dokl. Akad. Nauk SSSR, 152, 1399 (1963). 65. F. Gutmann and L. E. Lyons, Organic Semiconductors, John Wiley and Sons Inc., New York, 1967. 66. P. Holzman, R. Morris, R. C. Jarnagin and M. Silver, Phys. Rev. Lett., 19, 506, 940 (1967). 67. A. Kawada and R. C. Jarnagin, J. Chem. Phys. , 44, 1919 (1966). 68. E. Courtens, A. Bergman and J. Jortner, Phys. Rev., 156,948 (1967). 69. M. Silver, D . Olness, M. Swicord and R. C. Jarnagin, Phys. Rev. Lett., 10, 12 (1963). 70. M. Pope, J. Burgos and J. Giachino, J. Chem. Phys., 43, 3367 (1965). 71. L. P. Gary, K. de Groot and R. C. Jarnagin, J. Chem. Phys., 49,1577 (1968). 72. A. Proch, M. Djibelian and S. Sullivan, J. Phys. Chem., 71, 3378 (1967). 73. K. Hoh, Chem. Phys. Lett., 1, 235 (1967). 74. E. Wasserman, R. W. Murray, W. A. Yager, A. M. Trozzolo and G. Smolisky, J. Am. Chem. Soc., 89, 5076 (1967). 75. K. Hoh, M. Konishi and N. Mataga, J. Chem. Phys., 48, 4789 (1968). 39. 40. 41. 42. 43. 44. 45.

6.18 References

299

76. W. A. Noyes, Jr. and I. Unger, Adv. Photochern. , 4, 49 (1966). 77. G. W. Robinson, The Triplet State, p. 213, Cambridge University Press, 1967. 78. F. M. Garforth, C. K. Ingold and H . G . Poole, J . Chern. Soc., p. 406 (1947); F. M. Garforth and C. K. Ingold, J. Chern. Soc., p. 417 (1948). 79. H. Ishikawa and W. A. Noyes, Jr. , J. Chern. Phys., 37, 583 (1962). 80. W. A. Noyes, Jr. , W. A. Mulac and D . A. Harter, J. Chern. Phys. , 44, 2100 (1966). 81. J. A. Poole, J. Phys. Chern ., 69, 1343 (1965) . 82. G. B. Kistiakowsky and C. S. Parmenter, J. Chern. Phys., 42, 2942 (1965). 83. E. M. Anderson and G. B. Kistiakowsky, J. Chern. Phys. , 48, 4787 (1968). 84. A. E. Douglas and C. W. Mathews, J. Chern. Phys., 48, 4788 (1968). 85. G. W. Robinson, J. Chern. Phys., 47, 1967 (1967). 86. c. S. Burton and W. A. Noyes, Jr., J. Chern. Phys., 49, 1705 (1968). 87. D . F . Evans, J. Chern. Soc., p. 2753 (1959); p. 1735 (1960). 88. G. M. Almy and P. R. Gillette, J. Chern. Phys., 11, 188 (1943). 89. R. B. Cundall and D. G. Milne, J. Arn. Chern. Soc., 83, 3902 (1961). 90. R. B. Cundall, Progress in Reaction Kinetics, 2, 165 (1963). 91. R. B. Cundall, F. J. Fletcher and D . G. Milne, J. Chern. Phys., 39, 3536 (1963); Trans. Faraday Soc., 60,1146 (1964). 92. R. B. Cundall and A. S. Davies, Trans. Faraday Soc. , 62, 1151 (1966). 93. R. B. Cundall, A. S. Davies and K. Dunnicliff, The Triplet State, p. 183, Cambridge University Press, 1967. 94. W. A. Noyes, Jr. and D. A. Harter, J. Chern. Phy s., 46, 674 (1967). 95. S. Sato, K. Kikuchi and M. Tanaka, J. Chern. Phys., 39, 239 (1963) . 96. G. A. Haminger, Jr. and E. K. C. Lee, J. Phys. Chern., 71, 3104 (1967). 97. C. S. Burton and W. A. Noyes, Jr. , J. Chern. Phys., 49,1705 (1968). 98. D . Phillips, J. Lemaire, C. Burton and W. A. Noyes, Jr., Adv. Photochern., 5, 329 (1968). 99. R. B. Cundall, K. Dunnicliff and A. J. R. Voss, Joint Ann. Mtg. Chern. Soc. and R. Inst. Chern., Nottingham, April 1969. 100. P. Sigal, J. Chern. Phys. , 42, 1953 (1965). 101. J. W. Donovan and A. B. F. Duncan, J. Chern. Phys., 35, 1389 (1961). 102. T. H . Chen and E. W. Schlag, Molecular Lurninescence, p. 381 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. 103. D. S. McClure, J. Chern. Phys., 17, 905 (1949). 104. A. A. Lamola, G. S. Hammond and F. B. Mallory, Photochern. Photobiol., 4, 259 (1965). 105. J. K. Foote, M. H. Mallon and J. N. Pitts, Jr., J. Arn. Chern. Soc., 88, 3698 (1966). 106. K. Shin do and S. Lipsky, J. Chern. Phys., 45, 2292 (1966). 107. H. R . Ward, J. S. Wishnok and P. D. Sherman, Jr., J. Arn. Chern. Soc., 89,162 (1967). 108. M. Bixon and J. Jortner, J. Chern. Phys., 48, 715 (1968). 109. R . Astier, A. Bokozba and Y. H . Meyer, Transitions Non Radiatives dans les Molecules, Paris, 1969; J. Chirn. Phys. (in press); R. Astier and Y. H. Meyer, Chern. Phys. Lett., 3,399 (1969). 110. J. B. Birks, Chern. Phys. Lett., 3, 567 (1969). 111. C. S. Parmenter and M. W. Schuyler, Transitions Non Radiatives dans les Molecules, Paris, 1969; J. Chirn. Phys. (in press); C. S. Parmenter and A. H. White, J. Chern. Phys. , 50, 1631 (1969).

300

The Triplet State 6.18

112. M. S. de Groot and J. H. van der Waals, Mol. Phys., 6, 545 (1963). 113. T. E. Martin and A. H. Kalantar, J. Chem. Phys., 48, 4996 (1968); 49, 235, 244 (1968). 114. T. E. Martin and A. H . Kalantar, Transitions Non Radiatives dans les Molecules, Paris, 1969; J. Chim. Phys. (in press). 115. F. Hirayama, J. Chem. Phys., 42, 3726 (1965). 116. M. F. O'Dwyer, M. A. El-Bayoumi and S. J. Strickler, J. Chem. Phys., 36, 1395 (1962). 117. G. C. Nieman, J. Chem. Phys., 50,1660,1674 (1969). 118. D. Lavalette, Chem. Phys. Lett., 3, 67 (1969). 119. D. R. Kearns and M. Calvin, J. Chem. Phys., 34, 2026 (1961). 120. A. KearveII and F. Wilkinson, Mol. Cryst., 4, 69 (1968). 121. J. L. Kropp and W. R. Dawson, Molecular Luminescence, p. 39 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. 122. G . F . Hatch, M. D. Erlitz and G. C. Nieman, Molecular Luminescence, p. 21 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969.

7 Excimers 7.1 Excimer fluorescence Pyrene in dilute solution exhibits a structured violet fluorescence emission band, with a 0 - 0 transition at Mo ~ 27,000 cm- I , characteristic of the excited molecule I M *, which has a fluorescence quantum efficiency qFM. As the molar concentration PM] of the solution is increased, the molecular fluorescence quantum yield decreases, according to the Stern-Volmer relation (J>

qFM

(7.1)

FM = 1 + PM]/ PM]h

where PM]h is the 'half-value' concentration at which (J>FM = 0·5 qFM. The parameter K (= 1/ [1 M]h) is the Stern-Volmer coefficient of concentration

quenching. The concentration quenching of the molecular fluorescence is accompanied by the appearance of a broad structureless blue fluorescence, the peak intensity of which is at an energy of Dm , about 6000 cm- I below Mo. The fluorescence spectra I of pyrene solutions of various concentrations are shown in Figure 7.1, in which the spectral intensities have been normalized to a common value of(J>FM (cf. Figure 4.5). The structureless emission band is due to the fluorescence of excited dimers D *), produced by the collisional interaction of excited molecules M*) and unexcited molecules

e

e

eM),

(7.2) No corresponding changes with increase in [I M] are observed in the solution absorption spectrum showing that the excited dimers are dissociated in the ground state. The term excimer was introduced by Stevens to describe an excited dimer which is dissociated in the ground state, to distinguish it from a normal dimer in an excited state. The excimer fluorescence quantum yield (J>FD increases with PM] according to the relation

(7.3)

302

Excimers 7.2

where qFD is the excimer fluorescence quantum efficiency, defined as the limiting value of

~

Q)

0::

( b)

8 6

4

2 0 6500

6000

5500

30 0 0

5000 Wave iength (,8.)

Figure 7.18 Phosphorescence spectra of (a) 2,2'-paracyciophane, and (b) 4,4'-paracyciophane, in EPA glass solution at 77°K (after Hillier, Glass and Rice 72)

-------------------, ' " 38

38,000

~

E ,u

2u

3E, u

E'9

i

~

82g

>.

E' Q)

c

Q)

c

20,000"

~ 'in c

o

..:: 10,000

25

30

35

Ring separation (II)

Figure 7.19 Triplet states of the benzene excimer. Theoretical energies of D6b benzene dimer as a function of interplanar separation. Low-energy components of excimer states of 3B!u, 3E!u and 3B2u molecular parentage (after Hillier, Glass and Rice72 )

7.18 Excimer Phosphorescence

347

of r > 2·5 A, the lowest dimer triplet state is found to be the 3B 2g state, originating from the 3B 1u La) state of benzene. The calculated energies for the 3B 2g state at r = 3 A and 3·5 A agree reasonably with the observed o - 0 transition energies in the phosphorescence spectra of 2,2'- and 4,4' -paracyclophane, respectively. The configuration interaction with the charge-resonance state produces a significant triplet excimer interaction potential, but this may be insufficient to counterbalance the intermolecular repulsive potential and yield an associated triplet excimer state of benzene. Indirect evidence for the possible occurrence of triplet excimers in liquid benzene has been obtained from studies of the sensitization of biacetyl phosphorescence,73 but spectroscopic evidence is currently lacking. The magnitude of the charge-resonance contribution to the excimer interaction potential increases with decrease in (J - A), the difference between the ionization potential (J) and electron affinity (A) of the molecule. A value of (J - A) = II eV was assumed in the calculations on benzene.72 Alkyl or halogen substitution in benzene lowers (I - A) (see Tables 9.5 and 9.6) and thereby increases the excimer interaction potential. This may account for the observation of excimer phosphorescence in the halo benzenes and some alkyl benzenes. 68.70-71 Photo-excited excimer phosphorescence from an aromatic hydrocarbon in fluid solution was first reported by Langelaar et a/Y, who observed extremely weak structureless bands in the phosphorescence spectra of naphthalene and phenanthrene in fluid ethanol solutions at reduced temperatures, which they attributed to excimer phosphorescence. Langelaar 58 has subsequently shown that the phenanthrene emission is due to an impurity, probably naphthalene, but he has confirmed that the structureless phosphorescence band in naphthalene persists after repeated purification. The spectroscopic data on the various emissions attributed to triplet excimers or dimers are summarized in Table 7.10. The quantum yield of molecular phosphorescence in fluid solution is low, and that of excimer phosphorescence is even lower, and near the limits of instrumental sensitivity. Langelaar 58 has obtained alternative kinetic evidence for triplet excimer formation

e

(7.98) in fluid solutions of aromatic hydrocarbons (naphthalene, phenanthrene, anthracene and pyrene) by observations of the concentration quenching of the 3M* decay time 'TT' It is observed that the 3M* decay parameter kT (= l /'TT) in deoxygenated ethanolic solutions of high purity is given by (7.99)

348

Excimers 7.18

where (kT)o is the limiting value of kT at low temperatures, kdiff

=

8RT 30001)

(7.58a)

is the rate of a diffusion-controlled collision process, and p, which is small, is the 3D* formation efficiency. Equation (7.99) predicts a linear dependence of kT on [I M] at a given temperature, and such behaviour has been observed 58 in ethanolic solutions of anthracene at 20°C and of phenanthrene at temperatures from -120°C to -60°C. Langelaar58 assumes that kdiff = p

=

k~iff exp (- WT//kT)

(7.61a)

p' exp (Wp/kT)

(7.100)

so that (7.99) becomes kT = (kT)o

+ [lM]p' k~iffexp [-(WT/ -

Wp)/kT]

(7.101)

The observed temperature dependence of kT at a given [I M] is consistent with (7.101), and the values of (WT/ - Wp ) obtained from the gradient of Arrhenius plots of 10gkT against liT are independent of [1M]. Table 7.11 lists the values of WT/ - Wp , WT/ (from the viscosity-temperature curve of ethanol), Wp , and p at 20°C obtained for ethanolic solutions of different hydrocarbons. An alternative explanation for the temperature dependence of kT is considered in §9.l2 (see page 630).

Excimers

349 Table 7.1 Excimer formation collision parameters (in cyclohexane at 20°C)6

Code

Solute

pajb

4.1

Pyrene

1'0

4.3

1 :2-Benzanthracene (BA)

0'4

4.3G

5-Methyl BA

0'6

4.3H

6-Methyl BA

0'45

4.3L

lO-MethyI BA

0'8

Excimers

350 Table 7.2 Activation energies of excimer formation

for pyrene in different solvents 9 Solvent

WOM (eV)

W1J (eV)

Hexane Acetone Ether Toluene Cyclohexane Ethanol

0'09 0'097 0'11 0'13 0'14 0'152

0'10 0'096 0'09 0'10 0'14 0'156

Table 7.3 Molecula r and excimer rate parameters, fluorescence quantum efficiencies and lifetimes in room temperature solution

trl ~

r:.

1"M

Code 1 lA 1D 2

2A 2B 2C

2D 3.1B

Compound Benzene Toluene p-Xylene Naphthalene

Solvent

qFM

(ns)

Hexane Hexane Hexane 95% EtOH Cyclohexane Hexane Toluene Liq. paraffin

0·055 0·12 0·20 0·12 0·19

26 39·2 2S 52 120 110 110 ]17

kM

1"0

kFM

(10 6 s-')

qFO

39 19·5 36 19·2 S·3 9·1 9·1 S·6

1·9 2·4 7·7 2·3 1·7

0·012 0·045

0·34

0·32

ko

k FO

(10 6 s-')

(12) (S3) 27-8 36

kOM

(1·0) 1·6 0·9

3·3 (15) 4·5 (16) (IS) (22)

1-1

3·2

0·25 0·09

300 (67) 220 (63) (56) (45)

1·1 0·4)

2·0

230

1·3

0-4

24 12 21 20 19 40

2·9 (2·2) 3-4 5·0 (5·3) (6·1)

55

IS

3·6

0·36

95% EtOH

0·30

44

23

6·S

(0·3)

Benzene Chloroform Diethyl ether p-Xylene Ethanol Toluene

0·75 0·54 0·62 0·69 0·82

3·5

Ref.

.

'"

a, b, c b,d a,b,c e

2·63 (S·6) (15) (12·5) (9·1)

42 S3 47 50 53 25

k MO

(10 9 M-' s- ') (10 6 S- l)

3S0 (117) (66) (SO) (110)

0·12 I-Methylnaphthalene 95% EtOH (O·IS) Toluene 0·16 2-Methylnaphthalene 95 % EtOH n-Heptane 0·25 1,6-DimethylCyclohexane (0·28) naphthalene Phenylcyclo- (0·15) hexane 0·20 95% EtOH 2,6-Dimethylnaphthalene 9,1O-Dimethylanthracene

(ns)

S· n>

f, g g g g

e f, g e f, h h h e e

0·24 0·1 0·21 0·34 0·13 16·2

62

~220

~

Ul ....

w

Table 7.3 (continued) TM

Code 3.1G

Compound

Solvent

qFM

9,10-Di-n-propylToluene 0·98 anthracene 3.1K 9-Acetoxyanthracene Toluene 0·26 3.1L 9-Anthracene Ethanol 0·07 carboxylic acid Pyrene 4.1 Cyclohexane 0·65 (0'50) Acetone 95% EtOH (0'44) 0·65 Ethanol 0·52 Toluene 0·51 Nonane Hexadecane 0-46 Paraffin oil 0·36 Crystal Benzene 4.1C 4-Methylpyrene Benzene 4.1D 3-Chloropyrene 4.1E 3-Bromopyrene Benzene 4.1F 3-Cyanopyrene Benzene 4.3 1 :2-Benzanthracene Cyclohexane 0·19 (BA) 4.3G 5-Methyl BA Cyclohexane 0·20 Cyclohexane 0·14 4.3H 6-Methyl BA Cyclohexane 0·25 4.3L 10-Methyl BA

kM

kFM

U\

N

TO

(106 S-I)

qFO

(ns)

68

67

0·28

-50

4·6 217 2 500

55 35

0·023 0·092

1·5 (1'5) (1'5) (1'4)

0·75 0·57 0·65 0·55 0·55 0·54 0·50 0·69 0·64

(ns) 14·7

450 330 290 (475)

90 30 3 25 44 43 56 54

2·25 3'0 3-4 (2'1)

11 33 330 40 22 23 18 18'5

ko

kFO

(10 6 S-I)

(20)

kOM

k MO

(109 M- 1 S-I) (10 6 S-I)

Ref. j, k

(5'6) 7

65 15·5 43·5 23 50 20 (53) (19)

11-6 13 13 (10'5)

6'7 14 7·0 6·0

6·5 12 7·0 8·3

m n n o,p q q

q

113

8·8

4·2

0·47

41

24

4·7 2'5 4·6

0-49 0·33 0·65

93 39 98

11 26 10

q r

5·5

11 5·3 8·5 6·6

10 9 7 10 2·9 H

3·0 5·4

s s 101 29 42 36

t"l l>


§.

., '" ~

(11)

rp-CH-rp I

No

~100

35460

trJ

(PC)

~

n

S· ."

.

rp

rIJ

(12)

~ -CH-CH2-4>

No

35460

Yes

35460

30030

5430

Yes

34970

30030

4940

39

11·7

Yes

35210

30030

5180

30

14·5

Yes

34970

30030

4940

13·5

15·4

PC

I

4>

(13)

~-(CH2h-CH-

2·7

10·0

I

4>

(14)

Y < C H 2)3-Q H3 C

(15)

Q FO =

(8.20)

kFoKe[lMJ/f3

and the total normal fluorescence quantum yield is

cJ> _ cJ> F-

-'M*

" ,""

,

cJ>

FM+

'-. "kMTTlr3Moj '-.

"-

"

OTT (+3 M*)

rM1

/' /'

""

L / /'

i

/'

/'

/' /

L /

/' / / k

/

/

TO

(- 'M ) kFD kGO I

I

I

k GTT [3M*J kPT (+ 3M*) 1 kGT I

I

I

I

I I 'M

k

(+3 M* )

I

I

'D*

MO

'-.

3M'~ I I I

['M"] (+ 'M)

k

"-

(8.21)

--:..-::-~=== -k (-'M) ---

'-. '-.

kTM "-

kFM kGM

_ kFM + kFO Ke[l MJ f3

FO -

I

t

i-

I I

I I

t

k (_'M)

~

I

i

2'M

Figure 8.3 Schematic diagram of rate processes involved in triplet-triplet association and P-type delayed fluorescence in concentrated fluid solutions. Solid lines, radiative transitions; broken lines, radiation less transitions Similarly the total triplet quantum yield, cJ>T, is the sum of two components, originating from 'M* and 'D*, respectively, (8.23) where cJ>TM = kTM/

f3

(8.23)

is the quantum yield of3M* from 'M*, and cJ>TO

= kTO Ke['MJ/f3

(8.24)

is the quantum yield of3M* from 'D*. In the observation of delayed luminescence the exciting light is cut off with a phosphoroscope disc (§6.4) or other form of shutter, after the initial

380

Delayed Luminescence 8.4

excitation which, if of sufficiently long duration , produces a triplet molar concentration of (8.25) The delayed emission is observed after an interval td, where 'TT> td > 'TM, 'To. The prompt fluorescence intensity is now negligible, and the delayed fluorescence and phosphorescence are observed. In the aromatic hydrocarbons E-type delayed fluorescence is negligible because LlST is large, but P-type delayed fluorescence is produced by 3M* - 3M* interaction. The dark period rate equations are as follows: d[i:;r*]

=

-(kM + kOM[iMD [iM*]

d[~*] = koM[i M] [i M*] d[3M*] dt

=

k TM [iM*]

+ kMO[iD*] + tkMTT PM*]2

(8.26)

(k o + k MO ) [i D*] + !kOTT [3M*]2

(8.27)

+ kTD[iD*] -

k T[3M*] - k TT [3M*]2

(8.28)

where kTT is the total rate parameter of 3M* - 3M* interaction, and kMTT and kOTT are the rate parameters of 3M* - 3M* interactions yielding IM* + 1M and ID*, respectively. The rate parameter of any 3M* - 3M* interactions yielding 3M* + 1M is included in k T • Equations (8.26)-(8.28) can be solved explicitly. I I Similar results are obtained more simply by assuming quasi-stationary conditions for [iM*] and [iD*]. This approximation is justified because kM' k o }> kT' kTT [3M*], the parameters which determine the overall decay of excitation in the system. Putting d[i M*]/dt = d[iD*]/dt = 0, and eliminating PM*F from (8.26) and (8.27), we obtain

kOTT (k o + k MO ) PD*] - kOM[iM] [IM*] - = -- kMTT (kM + kOM[iMD [iM*] - kMO[D*]

IX = -

(8.29)

In terms of the parameter IX, the ratio of the quantum intensities 1$0, I$M of the delayed excimer and molecular fluorescences, respectively, is given by,12

1$0 I$M =

=

kFO[ID*] kFMPM*]

(8.30)

kFD {lXkM + (I + lX)kOM[iM]} kFM ko + (1 + IX) k MO

(8.31 )

K2

+ K)[iM]

(8.32)

8.4 Triplet-Triplet Interaction in Concentrated Fluid Solutions

381

If Ct. = 0, (8.31) reduces to

k FO kOM[1 M] = KI [I M] kFM (ko + k MO )

=

iJ>FO iJ>FM

(8.33)

which is the equation (7.15) describing the prompt fluorescence. In general Ct. is the ratio of the probabilities of the initial formation of ID* and IM* by a particular process, and equation (8.31) can be applied to any such process, irrespective of the mechanism. With photo-excitation of the prompt fluorescence Ct. = 0, since only 1M* is initially excited. With P-type delayed fluorescence it is observed '" 13 that Ito iJ>FO - > -ItM iJ>FM

(8.34)

demonstrating that Ct. > 0. Initially, Parker and Hatchard '3 assumed from the observation of (8.34) for pyrene solutions in ethanol that a = cx:> , i.e. that 3M* - 3M* interaction results in the initial formation of ID* only, but a subsequent analysis l2 showed that Ct. = 2 for this system at room temperature. The dark period decay of [3M*] is described by (8.28). If we neglect kTM PM*] and kTD PD*] in comparison with the other terms in (8.28), it reduces to (8.35) so that,9 [3M*]

=

1+

[3M*] e - kT1 [3M*]s(kTTi k T )(l- e - kT1)

From (8.26), (8.27) and (8.35), it can be shown that " [IM*] = R M [3M*]2 PD*]

=

Ro[3M*]2

(8.36)

(8.37) (8.38)

where R

_ {kMTT + kOTTkMO/(ko M -

R _ {kMTTKe P M] 0-

2(3

+ kMO)}

+ kOTT(kM + kOMP MD/(ko + kMO)} ~

(8.39) (8.40)

Substitution of (8.37)-(8.40) into (8.30) yields equation (8.31) for (Ito/lffM)' showing that the ratio of the quantum intensities of the delayed ID* and 1 M* fluorescences is independent of 10 and t.

382

Delayed Luminescence 8.4

Two limiting cases of (S.35) will be considered: (A) k T ;;,. kTT [3M*], corresponding to small 1o, small [3M*]s and/or large t; and (B) kT ~ kTT [3M*], corresponding to large 1o, large [3M*]s and/or small t. In case A, (S.36) reduces to

(S.4l) so that the quantum intensities of phosphorescence (lPT), delayed molecular fluorescence (l#M) and delayed excimer fluorescence (l#o) at time tare, respectively, from (S.37), (S.3S) and (S.4l). fPT = kpT[3M*]se- kTt = OPT e-kT t

(S.42)

nM = kFMRM[3M*];e-2kTt = O~Me-2kTt

(S.43)

I~o

= k F O Ro[3 M*]; e- 2kT t =

O~o e- 2kT t

The initial luminescence quantum intensities extrapolated to t respectively,

8pT = k pT[3M*]s = qPT CPT 1o = CPPT fo 8~M

8~o

(S.44) =

0 are,

(S.45a) (S.45b)

k FMRMPM*];

(S.46a)

_- k FM R M (CPT 10)2 -kT

(S.46b)

= k FO R o [3M*];

(S.47a)

= kFORo(cp;:Or

(S.47b)

=

The (a) equations are valid in general; the (b) equations are only valid if the excitation conditions are such that (S.25) is applicable. The total yields of the three luminescences are, respectively, rPPT =

1°

IpTdt = iT [3M*]s = qpTPM*]s

(S.4S)

T

(S.49)

(S.50)

8.4 Triplet-Triplet Interaction in Concentrated Fluid Solutions

The following features of case A (kT

}>

383

kTT[3 M *]) may be noted:

(i) the phosphorescence intensity (1m BpT ) and yield (fpT) are proportional to PM*]., and hence to 10 ; (ii) the delayed fluorescence intensities (ltM' B~M' Ito, B~o) and yields (f~M' f~o) are proportional to [3M*];, and hence to I~ and to B~T; and (iii) the phosphorescence decays exponentially with a lifetime of 'TT, and the delayed fluorescences decay exponentially with a common lifetime of t'TT. In case B (kT

T are plotted in Figure 8.9. At low temperatures, ID* formation is negligible, and the decrease in cJ>T ( = cJ>TM) with decrease in Tis due to the increase of cJ>FM (= qFM) towards its limiting low-temperature value of o kFM 1 ffiO (8.80) qFM = k + kO = - '¥TM FM

TM

Limiting low-temperature values of q~M ~ 0·98, cJ>~M ~ 0'02, k~M ~ 3 X 104 S- I , are estimated for pyrene in propylene glycoLl) As the temperature is increased and 1D* formation becomes significant, an increasing fraction of the initial excitation is dissipated radiationlessly via 1 D* without the formation of 3M*. This accounts qualitatively for the decrease in cJ>T with increase in T at higher temperatures (Figure 8.9). (iv) Sensitized P-type delayedfluorescence Parker and Joyce 20 • 32-33 have determined relative values of cJ>TM from observations of the sensitized P-type delayed fluorescence of aromatic hydrocarbons in fluid solution at room temperature. A solution containing a donor compound M (e.g. anthracene), of triplet energy Ef, is excited via its singlet state to yield its P-type delayed fluorescence. A small concentration of an acceptor compound Y (e.g. perylene), of triplet energy Ei < E¥ is added to the solution. It is observed that the P-type delayed fluorescence of M is completely quenched by the energy transfer process (§11.5)

(8.81) and it is replaced by the sensitized P-type delayed fluorescence of Y, produced by the process (8.82) Under these conditions the initial quantum intensity B~dy of the sensitized delayed fluorescence of Y is given by an equation, analogous to that for the directly excited delayed fluorescence (8.60), namely Bsd

FY

1FY

=

t kYTT 1o(cJ>TM T,¥)2

(8.83)

where 1Fy (= qFY1o) is the prompt fluorescence quantum intensity of Y, qFY is the fluorescence quantum efficiency of Y, 10 is the incident light intensity absorbed by M, cJ>TM is the triplet quantum yield of M, kYTT (=PykdiCC) is the rate parameter of process (8.82) and Tf is the triplet lifetime of Y (equal to twice the lifetime of its delayed fluorescence). Observations were made 32 on solutions containing [M] = 5 x 10-5 M anthracene, and [Y] = 10-5 perylene, excited by light of366 nm wavelength, and the results were analysed assuming cJ>TM = 0·70 for anthracene. Values

8.10 Recombination Luminescence

397

of py = 0'026, 0·012, and 0·012 were obtained for solutions in ethanol, n-hexane and cyclohexane, respectively. The normal P-type delayed fluorescence of 10-5 M perylene solutions, excited by light of 436 nm wavelength, was then observed, and the results analysed from the equation,

eh _ lk I (m Y)2 -[ - 2 YTT 0 'VTyTT

(8.60a)

FY

using the values of k YTT previously determined. In this manner values of the perylene triplet quantum yield tPTY = 0'0088, 0·015 and 0·014 were obtained for solutions in ethanol, n-hexane and cyclohexane, respectively. The major difficulty in these interesting pioneer experiments is the determination of the initial delayed fluorescence intensities e~dy and e~y by spectrophosphorimetry (§6.4). This may account for the low values of PY and tPTY obtained. The technique has been extended 33 to obtain relative values of the triplet quantum yield tPTM of different donors, from the relative intensity e~dy of the sensitized delayed fluorescence of a common acceptor Y. For two donors, indicated by subscripts 1 and 2, under identical conditions,

(tPTM)1 = {(e~Y)I}1/2 (tPTMh

(e~~h

(8.84)

The values of tPTM for various aromatic hydrocarbons obtained from sensitized P-type delayed fluorescence measurements, taking tPTM = 0·70 for anthracene at 20 e, are included in Table 6.l. D

8.10 Recombination luminescence

Ionization of an aromatic molecule I M can be produced (a) by direct photo-ionization 1M

+ hv ---? 2M+ + 2e-

(8.85)

provided that hv > I, the molecular ionization potential in the medium; (b) by biphotonic ionization via 3M*, provided that hv > (l- ET ), the 3M* ionization potential (§6.15); (c) by biphotonic ionization via IM*, provided that Es > 0'51; (d) by ionizing radiations, e.g. X-rays, y-rays, etc.; (e) by dissociation of a donor-acceptor complex or exciplex (§9.9); or (f) by electrolysis (§7.17) or chemical reaction. When the ionization occurs in a solid or in a rigid glass solution at low temperatures, the recombination of the molecular ion (2M+) and electron

398

Delayed Luminescence 8.10

(2e-) is inhibited by the trapping or solvation of the electron, and by the immobility of the trapped electron and the ion. Ion recombination 2M+ + 2e-

~

IM*

(8.86)

2M + + 2e-

~

3M*

(8.87)

yields molecules in their excited singlet and triplet states, IM* and 3M*, respectively. If the four alternative states 1,3M* are formed with equal probability, then the rate of 3M* formation will be three times that of 1 M* formation. Brocklehurst et al. 34 have concluded that the relative yields of 3M* and 1 M* in the y-irradiation of low-temperature rigid glass solutions of naphthalene are in the approximate ratio of 3: 1, consistent with multiplicity weighting. Brocklehurst41 has discussed the factors which may reduce the ratio below 3: 1. The IM* and 3M* luminescences, resulting from ion recombination, are referred to as recombination fluorescence and recombination phosphorescence, respectively. The ion recombination is accelerated by heating the system, and the resultant recombination luminescence is known as thermoluminescence. If the heating is applied at a controlled steady rate, the curve relating the thermoluminescence intensity to the temperature is known as a glow curve. Glow curves commonly exhibit one or more maxima (glow peaks) at temperatures at which the thermal energy (kT) approximates to the electron trap depth. Similar thermoluminescence is common in inorganic phosphor systems, and the appropriate theory has been developed relating the glow curve observed at a given heating rate to the depths and distribution of the electron traps.35 Recombination luminescence can also be stimulated by infra-red illumination of an irradiated specimen. Parker 6 has reviewed work on recombination luminescence in organic systems. One of the earlier studies was by Debye and Edwards 36 who observed a very long-lived (> 102 s) luminescence from irradiated solutions of phenol, toluidine and other compounds in rigid glasses at 77°K. The non-exponential luminescence decay was interpreted as due to initial photoionization and subsequent diffusion of electrons, thermally released from traps, back to the molecular ions. Linschitz et al. 37 observed the absorption spectra of solutions of lithium in mixed amine glasses at low temperatures. These show an intense peak at~600 nm, with a weaker continuum extending into the infra-red. Illumination with light of shorter wavelength decreases the intensity of the 600 nm band and increases that of the longer wavelength continuum. The 600 nm band was identified as due to solvated electrons in relatively deep traps, and the continuum to electrons in shallower traps. Irradiation of lowtemperature rigid glass solutions of lithium diphenylamide, N-lithium

8.10 Recombination Luminescence

399

carbazole and similar compounds causes a diminution of the molecular absorption intensity and the appearance of two new absorption band systems, due to the solvated electrons and the molecular ions, respectively. On warming the irradiated solution, the intensities of these two absorption band systems decrease, and a recombination luminescence with the same spectrum as the 3M* phosphorescence is observed, corresponding to process (8.87). No recombination fluorescence corresponding to (8.86) is observed. Albrecht and co-workers38 made similar studies on irradiated solutions of N,N'-tetramethyl-p-phenylenediamine and other compounds in hydrocarbon glasses at 7rK. Subsequent infra-red illumination yielded both recombination 3M* phosphorescence and IM* fluorescence. The intensity ratio IhilFM of the two recombination luminescences was, however, greater than the intensity ratio IpT/IFM of the corresponding normal emissions, showing that (8.87) is more probable than (8.86). With acriflavin and related dyestuffs in EPA glass solutions at 77°K, Lim and co-workers 39 observed a delayed fluorescence emission with a lifetime of several seconds, and a transient absorption which they assigned to molecular ions formed by photo-ionization. After an initial non-exponential decay, the fluorescence and the 2M + absorption decayed exponentially at the same rate. The integrated delayed fluorescence intensity and the initial 2M + absorption intensity are proportional to the intensity of the exciting light, and it was concluded that the photo-ionization occurs by a one-photon process. The results were explained in terms of a model earlier suggested by Albrecht et ai.,38 although the latter have subsequently reinterpreted their data in terms of a biphotonic process. 40 The evidence for biphotonic photo-ionization has been discussed in §6.15.

Delayed Luminescence

400

Table 8.1 Pyrene in ethanol solution at 20 e. Quantum yields of triplet formation (f/>T)' molecular fluorescence (f/>FM) and excimer fluorescence (f/>FD)13. 31 o

+ f/>FM + f/>FD)

Pyrene concentration PM]

f/>T

f/>FM

f/>FD

Infinite di lution

0'38

0'65

0

1'03

2 x 10-5 M

0'38

0'63

0'02

1'03

10-4 M

0'33

0'52

0'08

0'93

3 x 10- 4 M

0'26

0'41

0'21

0'88

10- 3 M

0' 185

0,21

0'38

0'775

(f/>T

8.11 References

401

8.11 References

1. 2. 3. 4. 5.

A. Jablonski, Nature, 131,839 (1933); Z. Phys. Lpz. , 94,38 (1935). W. L. Levshin and L. A. Vinokurov, Phys. Z. Sow., 10, 10 (1936). G. N. Lewis, D. Lipkin and T. T. Magel, J. Am. Chem. Soc., 63, 3005 (1941). G. N . Lewis and M. Kasha, J. Am. Chem. Soc., 66, 2100 (1944). c. A. Parker, Advances in Photochemistry, Vol. 2 (Ed. W. A. Noyes, G. S. Hammond and J. N. Pitts), lnterscience, New York, 1964. 6. C. A. Parker, The Triplet State, p. 353, Cambridge University Press, 1967. 7. J. B. Birks, Progress if! Reaction Kinetics, Vol. 5 (Ed. G. Porter), Pergamon Press, Oxford, 1970. 8. C. A. Parker and C. G. Hatchard, Trans. Faraday Soc. , 57, 1894 (1961); J. Phys. Chem., 66, 2506 (1962). 9. J. B. Birks and J. Grzywacz, Chem. Phys. Lett., 1, 187 (1967). 10. J. B. Birks and G . F . Moore, The Triplet State, p. 407, Cambridge University Press, 1967. 11 . J. B. Birks, G. F. Moore and I. H. Munro, Spectrochim. Acta, 22, 323 (1966). 12. J. B. Birks, J. Phys. Chem., 67, 2199 (1963); 68, 439 (1964). 13. c. A. Parker and C. G . Hatchard, Trans. Faraday Soc., 59, 284 (1963). 14. C. A. Parker and C. G. Hatchard, Proc. Chem. Soc. , p. 147 (1962); Proc. Roy. Soc. A, 269, 574 (1962). 15. J. B. Birks, B. N. Srinivasan and S. P. McGlynn, J. Mol. Spectrosc., 27, 266 (1968). 16. G. F. Moore and I. H . Munro, Spectrochim. Acta, 23A, 1291 (1967). 17. B. Stevens and M. I. Ban, Mol. Cryst., 4, 173 (1968). 18. C. A. Parker, Nature, 200, 231 (1963). 19. C. Tanaka, J. Tanaka, E. Hutton and B. Stevens, Nature, 198, 1192 (1963). 20. C. A. Parker and T. A. Joyce, Chem. Comm., p. 744 (1967). 21. B. Stevens and M. S. Walker, Proc. Roy. Soc. A, 281, 420 (1964). 22. S. Czarnecki, Bull. Acad. Polan. Sci. Ser. Math. Astron. Phys., 9, 561 (1961). 23. B. Muel, C.R. Acad. Sci. Paris, 255, 3149 (1962). 24. T. Azumi and S. P. McGlynn,J. Chem. Phys. , 38, 2773 (1963); 39,1186 (1963). 25. C. A. Parker, Trans. Faraday Soc. , 60, 1998 (1964). 26. M. A. EI-Sayed, J. Opt. Soc. Amer., 53, 797 (1963). 27. K. R. Naqvi, Chem. Phys. Lett. , 1, 497 (1967). 28. J. B. Birks, Chem. Phys. Lett., 2, 417 (1968) . 29. J. B. Birks, Phys. Lett. , 24A, 479 (1967) . 30. K. R. Naqvi, Chem. Phys. Lett. , 1, 561 (1968). 31. T. Medinger and F. Wilkinson, Trans. Faraday Soc., 62, 1785 (1966). 32. C. A. Parker and T. A. Joyce, Chem. Comm., p. 108 (1966). 33. C. A. Parke~ and T. A. Joyce, Chem. Comm., p. 234 (1966). 34. B. Brocklehurst, G. Porter and J. M. Yates, J. Phys. Chem., 68, 203 (1964). 35. G . F. J. Garlick, Luminescent Materials, University Press, Oxford, 1949. 36. P. Debye and J. O. Edwards, J. Chem. Phys., 20, 236 (1952) . 37. H. Linschitz, M. G. Berry and D. Schweitzer, J. Am. Chem. Soc., 76, 5833 (1954). 38. W. C. Meyer and A. C. Albrecht, J. Phys. Chem., 66,1168 (1962); E. Dolan and A. C. Albrecht, J. Chem. Phys., 37, 1149 (1962); 38,567 (1963); W. M. McClain and A. C. Albrecht, J. Chern. Phys. , 43, 465 (1965).

402

Delayed Luminescence 8.11

39. E. C. LimandG. W. Swenson,J. Chern.Phys., 36,118 (1962);39, 2768 (1963); E. C. Lim and W. Y. Wen, J. Chern. Phys., 39, 847 (1963); E. C. Lim, C. P. Lazzara, M. Y. Yang and G. W. Swenson, J. Chern. Phys., 43, 970 (1965). 40. K. D. Cadogan and A. C. Albrecht, J. Chern. Phys., 43, 2550 (1965). 41. B. Brocklehurst, Nature, 221, 921 (1969). 42. M. Zander, Naturwiss., 47, 443 (1960).

9 Molecular complexes

and exciplexes 9.1 Donor-acceptor complexes

If an electron acceptor A, i.e. a Lewis acid, is added to a solution of an aromatic hydrocarbon, which is an electron donor D , i.e. a relative Lewis base, a new optical absorption band, which is characteristic of neither A nor D, is commonly observed. This is known as a charge-transfer (CT) I

0·6

I

;

I

III

E CT

>.

"in

c

"

"0

o

0-4 -

~

Ci

o

0 "2 -

Wavenumber ( 100 crn- 1 )

Figure 9.1 Charge-transfer absorption spectrum of donor-acceptor complex of 1,4-dimethylnaphthalene andp-chloranil (after Aladekomo and Birks l )

absorption transition, and it is attributed to a donor-acceptor (DA) complex formed by the partial or complete transfer of an electron from D to A. Figure 9.1 shows a typical CT absorption band. l Common electron acceptors used in the study of the CT absorption spectra of aromatic 14

404

Molecular Complexes and Exciplexes 9.1

hydrocarbons include p-chloranil, 1,3,5-trinitrobenzene and iodine. Experimental values of the electron affinity (AA) of these and other acceptors are listed in Table 9.1. A fuller compilation of electron affinities has been given by Christophorou and Compton. 2 The theory of donor-acceptor interaction and CT spectra has been developed by Mulliken in a series of papers. 3 The ground-state wavefunction of the DA complex may be written as (9.1) where fo is the no-bond wavefunction of the DA structure, and fl is the dative-bond wavefunction for the D +A - structure, in which an electron is transferred from D to A. The corresponding wavefunction of the excited state of the DA complex is (9.2) For a weak DA complex, a* ~ a ~ 1 and b* ~ b ~ O. The fN -';> fE transition is thus appropriately described as a charge-transfer transition , since it corresponds approximately to a fo(DA) -';> fl(D +A - ) transition. It is, however, incorrect to describe the ground-state DA complex as a chargetransfer complex, as is commonly done. The ratio

b2 a +b 2

A=2 --

(9.3)

determines the fractional contribution of the D +A- structure to the groundstate, and this fractional ionic character can vary from A = 0 for no chargetransfer to A = 1 for complete electron transfer. The ground-state energy (WN ) of the DA complex is given by3-4

W - W _ (HOI - Wo S)2 N0 (WI - W o)

(9.4)

Wo and WI are the energies of the DA and D +A - structures, respectively, and HOI and S are the interaction energy and overlap of the two structures, respectively, which are given by

I foHfodr WI = I flHfldr HOI = I fl Hfodr s = I fl fodr Wo =

(9.5) (9.6) (9.7) (9.8)

9.1 Donor-Acceptor Complexes

405

where H is the Hamiltonian of the entire set of nuclei and electrons which comprise the complex. The excited-state energy (WE) of the DA complex is W, - W E -

I

+

(HoI - WI S)2 (WI - W o)

(9.9)

The ratios of the coefficients in (9.1) and (9.2) are given by b a

(HoI - WaS)

(WI

-

(9.10)

Wo)

b* (HoI - WI S) a* = - (WI - W o)

(9.11)

The coefficients a, b, a* and b* for various DA complexes have been evaluated from their dipole moments. 4 - 5 In a complex of a nonpolar donor with a nonpolar acceptor, the no-bond structure ~o(DA) has a negligible dipole moment 1L0 (~O) , but the dative bond structure ~I(D + A-) has a finite dipole moment ILl (~erDA), directed from D to A, where e is the electronic charge and rDA is the equilibrium separation of the two components in the complex. The dipole moment of the DA complex is given b y 3-4 (9.12) where rj is the vector coordinate of the ith electron. Hence, from (9.]) and (9.12), for 1L0 = 0, (9.13) i1-N = ILl (b 2 + abS) Application to (9.1) and (9.2) of the orthonormality conditions

J~~ dT = J~~ dT =

J~N~EdT

=

1

0

(9.14) (9.15)

yields the relations a 2 + 2abS + b 2 = a*2 - 2a* b* S + b*2 = 1 a*(b

+ as) =

b*(bS + a)

(9.16) (9.17)

Each of the parameters ILN, ILl and S may be either determined or estimated, so that the coefficients, a, b, a* and b* can be calculated from (9.13), (9.16) and (9.17). Table 9.2 lists the values of the dipole moment, the wavefunction coefficients, and the fractional ionic character A (9.3) thus obtained for various DA complexes. 4 - 5

Molecular Complexes and Exciplexes 9.2

406

9.2 Charge-transfer absorption The energy ECT of the peak of the Ij;N --+ Ij;E charge-transfer absorption transition is given by (9.18) E CT = WE - W N

_ W _ W -

I

0

+

(HoI - WI S)2 + (HoI - W O S)2 (WI - W o)

(9.19)

Figure 9.2 shows diagrammatically the potential energy curves of a DA complex as a function of the intermolecular distance r. The curves Wo(r)

\ \

t

WE (r )

\

/'

\.\'1 (r) \

/'

\

\

,

'-

/

- - / - - - - --1.-+-__-+_ WE . : :-

"

-

-

-

-

-

_

_

I1.. ' ---,..-

W1

o

o

co (--+

Figure 9.2 Schematic diagram of potential energy W of DA complex against intermolecular separation distance r. Wo(r), DA structure; WI(r), D +A - structure; WN(r), DA complex ground state; WEer), DA complex excited state; W o, WI> W N, WE, potentials at equilibrium separation, rOA; E eT , CT transition energy; 10 , donor ionization potential; AA, acceptor electron affinity and WI(r) represent the energies of the DA and D +A-structures, respectively. The curves WN(r) and WEer) represent the energies of the DA complex in the ground and excited states, respectively. Wo, W" WN and WE are the corresponding energies at rDA, the equilibrium separation of

9.2 Charge-Transfer Absorption

407

the ground state DA complex. ECT corresponds to the vertical FranckCondon WN -?- WE transition. From the diagram WI - Wo

=

10 - AA - (LlEO+A- - LlEoA )

(9.20)

=

10 - AA - LI

(9.21)

where /0 is the ionization potential of D, AA is the electron affinity of A, LI Eo+A- is the energy of formation of the D +A - structure and LI EOA is the energy of formation of the DA structure. Equation (9.19) can thus be rewritten as (9.20) Alternatively, from Figure 9.2, we may write ECT = WE - WN = 10 - AA - (LlEE - LIEN) =Io-AA -

c

(9.21)

where LlEE and LIEN are the energies of formation of the DA complex in the excited and ground states, respectively, and C is their difference. Numerous observations have been made of ECT for the DA complexes formed by a series of different donors D with a common acceptor A in a common solvent, and Briegleb 5 has compiled extensive lists of such data. Table 9.3 lists experimental values of ECT and E(CT)max. the maximum molar extinction coefficient of the CT transition , for the DA complexes formed by the aromatic hydrocarbons with three acceptors, iodine, p-chloranil and 1,3,5-trinitrobenzene. The solvent was carbon tetrachloride, except where otherwise indicated . The values of ECT decrease with increase in the electron affinity AA of the acceptor (9.21), and this can be used to estimate the relative values of AA for different acceptors. There are, however, discrepancies between the absolute values of A Aobtained by different observers (Table 9.1) associated with the difficulties in estimating the parameter C. Normally the CT transition consists of a single broad structureless band, but in some DA complexes two or more such bands are observed, as indicated in Table 9.3. The lowest energy band corresponds to ECT (9.20), and the other bands are attributed to transitions to higher excited states of the DA complex. Equation (9.20) predicts a monotonic parabolic relation between ECT and , Jo for a common acceptor and solvent, provided that (AA + LI) and 2fJ2 remain constant, as might be expected for a related series of weak DA complexes. Briegleb 5 has analysed extensive data on several such series of

Molecular Complexes and Exciplexes 9.2

408

DA complexes, and he has obtained good agreement with (9.20), taking the empirical values of (AA + LJ) and 2f32 for different acceptors, listed in Table 9.4. The donor ionization potentials cover a relatively narrow range: for the aromatic hydrocarbons 10 ~ 7 eV to 9·2 eV. This accounts for the linear relation between ECT and ID observed by McConnell et al. 6 and others for a series of DA complexes with a common acceptor: (9.22)

ECT=A'ID-B'

The empirical relation (9.22) is an approximation to the theoretical relation (9.20), and it may be expected to be valid only over a limited range of 10 • The data of Briegleb,5 considered above, are reasonably consistent with (9.22), with the empirical values of A' and B' listed in Table 9.4. The linear relation (9.22) has been verified for many sets of DA complexes formed by related series of donors with a common acceptor in a given solvent. The few deviations that occur are usually due to the inclusion of an alien donor of different molecular structure, e.g. triethylamine in a series of aromatic hydrocarbons. Another potential source of error in the comparison of the experimental ECT values with (9.20) or (9.22) is the uncertainty in the value of I D • Reliable ionization potentials have been obtained by photoionization measurements on vapours of many of the lighter molecules (see Table 9.5), but direct experimental 10 data are lacking for most of the heavier molecules. For the aromatic hydrocarbons, Briegleb S used the theoretical values of 10 evaluated by Hedges and Matsen,1 normalized to the experimental 10 value for naphthalene, and other observers have used a similar procedure in the analysis of their data. Foster8 measured ECT for carbon tetrachloride solutions of three series of DA complexes, formed by seven donors for which reliable experimental ID values are known (benzene, toluene, m-xylene, mesitylene, naphthalene, I-methylnaphthalene and aniline) with three different acceptors. He observed the following linear relations between 10 and ECT for the various acceptors: p-Chloranil

10 = 5·13

+ I·13ECT

(eV)

(9.23)

p- Benzoquinone

10 = 4·61

+ I·07EcT

(eV)

(9.24)

1,3,5-Trinitrobenzene

10 = 4·25

+ 1·13EcT

(eV)

(9.25)

Applying these empirical relations to the DA complexes formed by other donors, he obtained values of 10 agreeing closely with those of Briegleb. 5 Birks and Slifkin 9 have subsequently used (9.23) to evaluate 10 for several

9.2 Charge-Transfer Absorption

409

polycyclic hydrocarbons. The experimental values of the ionization potentials of aromatic molecules determined by this and other methods are listed in Table 9.5. For the benzene derivatives the values of I determined by photoionization are ~0'4 eV less than those determined by electron impact. For naphthalene and the higher polycyclic hydrocarbons the values of I determined by the different methods agree within the experimental error. The experimental values are generally higher than the theoretical values of Hedges and Matsen. 7 Gutmann and Lyons!O have compiled a list of the ionization potentials of other organic molecules and radicals. The electron affinity A of a molecule is a much more difficult parameter to determine than the ionization potential. Christophorou and Compton 2 have reviewed the different methods. Table 9.6, which is based on their compilation, lists the theoretical and experimental values of the electron affinity of aromatic molecules. The CT transition moment is given by3 (9.26) ~

a* b(/1-! - /1-0)

+ (aa* -

bb*) (/1-01 - /1-0 S)

(9.27)

where (9.28) is the transition moment between the no-bond DA structure and the dativebond D +A-structure. For a DA complex between two non-polar molecules, /1-0 ~ 0, and (9.27) reduces to /1-EN ~ a* b/1-1

+ (aa* -

bb*) /1-01

(9.29)

/1-1, the dipole moment of the D +A-structure, is directed along the axis of the complex. /1-01 is equivalent to the dipole produced by transfer of an

amount of charge eS from D to about halfway between D and A,3-4 so that /1-01 ~ S/1-d2 and (9.29) becomes /1-EN

~ [a* b + ~ (aa* -

bb*)] /1-1

(9.30)

The 1: 1 DA complexes of aromatic molecules with the aromatic acceptors, p-chloranil and I ,3,5-trinitrobenzene, form single crystals in which the molecular planes of the components are parallel. Nakamoto!! and Lower et al. !4 have studied the optical dichroism of single crystals of such complexes. The CT absorption transition /1-EN is observed to be polarized along the molecular z-axis, perpendicular to the molecular plane, i.e. in the /1-1 direction. This is in contrast to the behaviour of a pure aromatic

410

Molecular Complexes and Exciplexes 9.3

molecular crystal, where the absorption is polarized in the molecular plane, and this provides clear evidence for the CT nature of the transition. Briegleb and Czekalla l3 have compared the experimental (J.) and theoretical (ft) values of the oscillator strength of the CT absorption transition ofDA complexes in solution.fe was evaluated from the integrated CT absorption intensity, using equation (3.49) with n = 1. J-tEN was evaluated from (9.30), using the wavefunction coefficients of Table 9.2 (ref. a), and ft was calculated from equation (3.52) with G = 1, J-tEN == M lu ' The values ofJ. andft agree within 30 %for the DA complexes of durene, hexamethylbenzene and naphthalene with 1,3,5-trinitrobenzene, p-chloranil and tetracyanoethylene. The experimental data so far considered are all consistent with the original Mulliken modeP of DA complexes and CT absorption, and they provide evidence for its validity. An extension of the model to account for other CT absorption phenomena will be considered in §9.4. 9.3 Kinetics of DA complexes AI: 1 DA complex is formed in solution by the reversible process D+A

~DA

(9.31)

and for an ideal solution, the molar equilibrium constant is [DA) Ke = [D) [A)

(9.32)

where square brackets indicate molar concentrations. For a weak complex [DA) the D +Awavefunction, and 0/0' the DA wavefunction, corresponding to an increase in the coefficient b. From (9.27) or (9.29), one would therefore expect an increase in (ECT)max (cc IfLENI2) with increase in B. Comparison of the data of Tables 9.3 and 9.7 shows that generally (ECT)max decreases with increase in B, contrary to the prediction of the original Mulliken modeP An extension of the model to account for this behaviour is considered in §9.4. 9.4 Contact CT absorption

Iodine in n-heptane shows an absorption band which starts around A and increases steadily at shorter wavelengthsY Iodine in the gas phase or in perfiuoroheptane does not absorb in this region. In a mixture of iodine, n-heptane and perfiuoroheptane the intensity of this absorption band is strictly proportional to the product of the iodine and heptane concentrations, showing that the absorption arises from chance contacts between the two molecular species. A Benesi-Hildebrand plot (9.36) gives a straight line of finite slope passing through the origin, corresponding to Ke = 0 (i.e. no complex formation) and ECT = w. Evans l5 proposed that the absorption is due to a contact charge-transfer transition occurring during collision between iodine and n-heptane molecules. Bromine and oxygen exhibit similar contact CT absorption bands in solution in saturated hydrocarbons. With the aromatic hydrocarbons and other donor molecules of lower ionization potential than the saturated hydrocarbons, iodine and bromine give bound DA complexes, as described in §§9.1 and 9.2. Oxygen with the aromatic hydrocarbons exhibits only contact CT absorption, characterized by Ke = 0 and the absence of a peak in the CT absorption spectrum. In the oxygen perturbation technique used for the study of So - T 1 absorption in aromatic hydrocarbons [§6.8 (i)), the vibrational structure of the O 2 enhanced So - Tl absorption spectrum of the hydrocarbon is superimposed on the structureless contact CT absorption spectrum (Figure 6.3). Slifkin and Allison l6 have measured the energy Eo of the onset of the contact CT absorption spectra of a wide range of donors with oxygen dissolved in chloroform under 120 atm. They compared Eo with the energy ECT of the peak of the CT absorption spectrum of the donor with p-chloranil in carbon tetrachloride. For donors of a given molecular group (e.g. aromatic hydrocarbons, aliphatic amines, aliphatic amides) they observed a constant difference between ECT and Eo. For the aromatic hydrocarbons, ECT - Eo = 0·107 eV, which, in conjunction with (9.23), gives the empirical relation (eV) ID = 5·24 + 1'13Eo (9.39) 2600

9.4 Contact CT Absorption

413

between the donor ionization potential 10 and Eo, a relation which they used to evaluate 10 for other aromatic hydrocarbons. On the Mulliken model there are two contributions to the CT transition moment (9.29) I1-EN ~ a* bl1-1 + (aa* - bb*) 11-01 In stable DA complexes (B> kT) the first term, which arises from the ground-stabilization b, is dominant. In contact DA complexes (B< kT) this term becomes negligible, and the contact CT absorption is attributed to the second term 11-0], which remains finite at the Van der Waals separation ofD and A. In the derivation of the Benesi-Hildebrand relation (9.36) which is used to determine Ke and ECT, it was implicitly assumed that the latter arises solely from stable DA complexes and thus corresponds to Ecomplex. Orgel and Mulliken l7 have considered a model allowing for the contribution to ECT due to contact CT interaction of uncomplexed acceptor molecules with the excess concentration of donor molecules. Each uncomplexed acceptor molecule is assumed to have random contact CT interaction with IX donor molecules, and Econtact is the mean molar extinction coefficient of all such contacts. Hence (9.40) ECT = EcomPlex(1 + piKe) where p = IXEcon,act/EcomPlex. Thus ECT > Ecomplex> because of the contribution due to contact CT absorption. For the DA complexes of the alkyl benzenes and iodine (Tables 9.3 and 9.7) ECT is observed to decrease with increase in B, i.e. with increase in K e • To obtain an increase of Ecompl ex with Band Ke consistent with the theoretical relation (9.29), it is necessary to assume that p ~ 5, i.e. that Econtact ~ Ecomplex> since IX ~ 6. On the Mulliken model it would be expected that Ecomplex> Econtact, since the former involves both terms of (9.29), while the latter involves only the smaller second term. A solution has been suggested by Murrell,18 who proposed that contact CT transitions derive additional intensity from excited states of the donor or acceptor. For the excited-state wavefunction of the contact DA complex he replaces (9.2) by fE(D, A) = a* fl(D +A -) - b* fo(DA) - c* fiD* A) - d* f3(DA *) (9.4l) Let 00 , OJ; and 0A, 01 be the ground (highest filled) and excited (lowest unfiIIed) electron orbitals of D and A, respectively (Figure 9.3). The D +Astate may be formed (i) from DA by electron transfer from 00 to 01, (ii) from D* A by electron transfer from OJ; to 01, or (iii) from DA * by electron transfer from 00 to 0A. The interaction between the D +A-and DA structures depends on the overlap S(Oo,01) of 00 and 01. Similarly the interaction

Molecular Complexes and Exciplexes 9.4

414

between D +A-and D * A depends on See:;,( 1) and that between D +Aand DA * depends on SeeD,eA)' The spatial extent of the excited-state orbitals exceeds that of the ground-state orbitals, so that at the Van der Waals contact between D and A, which is determined by the exchange

e; - r': 80~

--O---O- 8A

0

A (i)

e;---o~ ----- e:

80

----

--O--O--8A

0*

et-----

~et

eo --O---O-~8A

A (i i)

A*

0 ( ii i )

Figure 9.3 Schematic diagram of D+A- state formation from (i) DA, (ii) D* A,

and (iii) DA * (after Murrell 18)

repulsive forces due to the overlap of their fully occupied orbitals, it is to be expected that (9.42) The degree of mixing of two states depends also on their energy difference. D* A and DA * are usually closer in energy than DA to D +A -, and this favours their introduction into fE (9.41). These considerations indicate tha Ic*1 > Ib* I, but that Id* 1is probably small, unless DA * is adjacent in energy to D +A-. MurreIl 18 proposed that the donor and acceptor excited states only contribute to the contact CT transition intensity Econtact . They do not contribute to the bound complex CT transition intensity Ecomplex for symmetry reasons. If the axis of the DA complex formed by an aromatic molecule is perpendicular to its molecular plane, the CT transition which is polarized along this axis cannot derive intensity from TT-TT* transitions, which are polarized perpendicular to this direction. The Murrell model thus provides a mechanism by which Econtact ~ Ecomplex> which would account for the anomalous decrease in ECT with increase in B. Christodouleas and McGlynn l9 have obtained evidence from spectroscopic and thermodynamic studies of naphthalene complexes with various acceptors which supports the Murrell proposal that the intensity of the CT

9.5 Luminescence of DA Complexes

415

transition is largely 'borrowed' from an intense transition of the naphthalene donor.

9.5 Luminescence of DA complexes

When a DA complex in solution or in the crystal phase is excited in its CT absorption band, the system exhibits two types of luminescence: (i) fluorescence characteristic of the DA complex, and corresponding to the tfE ---7 tfN transition; and (ii) phosphorescence, which may be characteristic of the donor D, the DA complex, or the acceptor A. 20 The DA complex fluorescence spectrum is a broad structureless band, while the donor phosphorescence spectrum often exhibits vibrational structure. The two emissions occur at similar energies, and the overlap of the two spectra led to an initial error by Moodie and Reid,21 who assigned the total luminescence to donor phosphorescence and thus obtained incorrect values for the energy ET of the first excited triplet states of anthracene and other compounds. (i) DA complex fluorescence. Systematic studies by Czekalla, Briegleb and co-workers 22 - 33 have clearly established the existence and nature of the DA complex fluorescence. The observed fluorescence lifetimes of the crystal DA complexes of several aromatic hydrocarbons with 1,3,5-trinitrobenzene (TNB) or tetrachlorophthalic anhydride (TCPA) are listed in Table 9.8. The lifetime T is characteristic of the complex, and it is unrelated to that of the aromatic donor. All the donor molecules, except anthracene, in Table 9.8, have SI = 1Lb and correspondingly long fluorescence lifetimes. The observed value of T = 2·6 ns for the hexamethylbenzene-TNB complex may be combined with the theoretical radiative lifetime TF = 20 ns evaluated from the integrated CT absorption spectrum to give an estimated DA complex fluorescence quantum efficiency qF ::: 0·13 at 293°K. Direct observations of qF for DA complexes appear to be lacking (see p. 632). The DA complex fluorescence spectra are structureless and they are approximately mirror-symmetric to the corresponding CT absorption spectra. Table 9.9 lists the absorption maximum (va), the fluorescence maximum (ve), and the mirror-symmetry wavenumber (v o ) (§4.2) of the DA complexes of several aromatic hydrocarbons in n-propylether-isopentane solutions at 77°K.23 For a given donor molecule, Va and Vf are observed to increase monotonically with the electron affinity AA of the acceptor, showing that the absorption and fluorescence are both characteristic of the DA complex. A similar correlation between Vf and Va is observed for

Molecular Complexes and Exciplexes 9.5

416

crystalline DA complexes of aromatic hydrocarbons with various acceptors at room temperature. 19 • 23 (ii) Phosphorescence. Czekalla et al. 24 compared the phosphorescence spectra at 77°K of the following systems: (a) n-propylether-isopentane solutions of aromatic hydrocarbons, excited via So - SI absorption and intersystem crossing; (b) similar solutions of DA complexes of these compounds with TCPA, excited via the CT absorption band ; and (c) crystals of these DA complexes, excited via the CT absorption band. For naphthalene, phenanthrene and I :2-benzanthracene, the phosphorescence spectra of the solution DA complexes (b) are similar to those of the donor (a), apart from some loss of vibrational structure, indicating they correspond to TI - So radiative transitions in the donor molecules. The spectra of the crystal DA complexes (c), which are red-shifted, show further loss of vibrational structure, but they appear to be characteristic of the donor in the crystal environment. For durene, the phosphorescence spectrum of the donor (a) exhibits vibrational structure, but those of the solution (b) and crystal (c) DA complexes, which are similar, are red-shifted by ~6000 cm- I, and are structureless. These have been subsequently attributed to DA complex phosphorescence by Iwata et al.,20 who have undertaken further studies which have clarified the behaviour.92 The phosphorescence from DA complex systems involves the following sequence of processes20 . 25 : (i) CT absorption into the first excited singlet state I(DA)* of the DA complex, from which the DA complex fluorescence occurs. (ii) Intersystem crossing from I(DA)* to the first excited triplet state 3(DA)* of the DA complex, followed by one of three alternative processes: (iii) dissociation of 3(DA)* into the locally-excited 3(D* A) state, leading to donor D*) phosphorescence; (iv) DA complex phosphorescence of 3(DA)*; or (v) dissociation of \DA)* into the locally-excited 3(DA*) state, leading to acceptor A *) phosphorescence.

e

e

The phosphorescence occurs from the lowest of the three alternative triplet states: 3(D* A), 3(DA)* or 3(DA*), corresponding to (iii), (iv) or (v), respectively. Iwata et aPO .92 observed the luminescence spectra of DA complexes of aromatic hydrocarbons with 1,2,4,5-tetracyanobenzene (TCNB), pyromellitic dianhydride (PMDA), phthalic anhydride (PA) and tetrachloro-

9.5 Luminescence of DA Complexes

417

phthalic anhydride (TCPA) in ethyl etherjisopentane (EP) solutions at 77°K. Figure 9.4 plots the phosphorescence spectra of TCNB and its complexes with alkyl benzenes in EP solutions at 77 oK. The phosphorescence spectra of the benzene-TCNB and toluene-TCNB complexes are similar to that of TCNB, apart from some loss of vibrational structure, and they are attributed to the phosphorescence of the acceptor (TCNB). The phosphorescence spectra of the TCNB complexes of mesitylene, durene and hexamethyl benzene are structureless. They differ from those of either the donor or the acceptor, and they are assigned to the CT phosphorescence

1!'

"Vi c:

.,

.s c:

o

:~

E w

Wavenumber (10 3 cm- 1)

Figure 9.4 Phosphorescence spectra of TCNB (1 ,2,4,5-tetracyanobenzene) complexes in EP solution at 77°K. 1, hexamethylbenzene-TCNB; 2, durene-TCNB; 3, mesitylene-TCNB; 4, tolueneTCNB; 5, benzene-TCNB; and 6, TCNB only (after Iwata, Tanaka and Nagakura 20) of the DA complex. The phosphorescence spectra of the TCNB complexes of phenanthrene and triphenylene are also structureless and, although they occur at similar energies to the structured donor phosphorescence, they also appear to be characteristic of the DA complex. In contrast, the phosphorescence spectrum of the naphthalene-TCNB complex is structured and similar to that of the donor. Thus, depending on the nature of the donor, three types of phosphorescence emission may be observed, characteristic of the donor, the DA complex or the acceptor. Beens and Weller 91 have discussed the conditions for the stability of DA complexes in the triplet state. Table 9.10 lists the following experimental data for DA complexes of aromatic compounds with various acceptors in rigid glass solutions at

418

Molecular Complexes and Exciplexes 9.S

77°K : (ET)D and (ET)A, the triplet energies of D and A, respectively; (vp)o and (vP)max> the 0 - 0 and peak energies of the phosphorescence spectrum of the DA complex, and its assignment; and (VF)max> the peak energy of the fluorescence spectrum of the DA complex. Table 9.ll presents experimental data 5 on the phosphorescence lifetimes at 77°K of the aromatic hydrocarbon donors in solution (TT)D and of the solution and crystal DA complexes with dichlorophthalic anhydride (DCPA), tetrachlorophthalic anhydride (TCPA) and tetrabromophthalic anhydride (TBPA). The reduction in TT in the DA complex systems is attributable to the combination of two effects: (J) spin-orbit coupling to the acceptor molecule which increases the probability of the spin-forbidden T 1 - So transition due to the external heavy-atom effect (§6.7) ; and (II) charge-transfer interaction between the donor and acceptor molecules which introduces CT character into the phosphorescence transition. In all the systems of Table 9.11 TT decreases systematically in the order: (i) pure solvent (no external heavy atoms); (ii) DCPA (two Cl atoms per acceptor molecule); (iii) TCPA (four Cl atoms per acceptor molecule); and (iv) TBPA (four Br atoms per acceptor molecules), demonstrating clearly the external heavy-atom effect (I). The effects are more pronounced in the crystal DA complexes, because of the higher acceptor concentration and higher degree of order, which facilitate intermolecular interactions. The higher aromatic hydrocarbons (n :> 2) all behave in a similar manner. The phosphorescence spectra of the DA complexes are characteristic of the donor, and it is concluded that for these systems the external heavy-atom effect (I) is primarily responsible for the reduction of TT' Eisenthal and El-Sayed 26 have observed the phosphorescence lifetimes of perprotonated and perdeuterated naphthalene and phenanthrene and their DA complexes with TCPA and TBPA in hydrocarbon glass solutions at 77°K. They analysed the data on the assumption that the heavy-atom effect modifies only the radiative transition probability k m which is the same in the protonated and deuterated compounds, but that it does not modify the radiationless transition probability k CT' For the uncomplexed protonated and deuterated compounds l /(T~)o = (k~)o = (kPT)o

+ (k~T)O

(9.43)

l/(T~)o = (k~)o = (kpT)o

+ (k8T)O

(9.44)

419

9.5 Luminescence of DA Complexes

and for their complexes J /T~

=

k~

k pT -I- k~T

(9.45)

l /T~

= k~ = kPT -I- kg T

(9.46)

=

If it is assumed that k~ = (k~T)O ' kg T = (kgT)o , then l /T~

= l /T~ -I- l /(T~) o - l /(T~)o

(9.47)

The values of T~ calculated from (9.47) are li sted in Table 9.12, and agree reasonably with the observed values. These data have been reanalysed taking (kpT)o = 0·03 S-I (§5.7), and the less restrictive condition that k~T oc kg T. The values of the rate parameters thus obtained are listed in Table 9.13. The results indicate that in the TBPA complexes kPT is increased by a factor of ~80, while k GT is increased by a factor of ~2. They are consistent with the previous analysis of the heavyatom effect in naphthalene (Table 6.5). The phosphorescence lifetimes of the DA complexes of the alkyl benzenes (Table 9.11) are much less than those of the donor molecules, and their red-shifted structureless spectra are characteristic of CT transitions, rather than donor molecular transitions. In these systems the CT interaction (II) is significant. The heavy-atom effect is still dominant, but it is more properly described as an internal effect, rather than an external effect, since the phosphorescence originates from the DA complex. Iwata et al. 20 have observed the phosphorescence lifetimes (TT)DA of the DA complexes of durene and hexamethylbenzene with TCNB and PA, two acceptors which do not contain heavy atoms, in EP solutions at 77°K. Their results (Table 9.14) show that (TT)DA is less than either (TT)D or (TT)A , the phosphorescence lifetimes of the donor and acceptor molecules, respectively, an effect which is attributable to CT interaction (II). Phosphorescence quantum efficiency measurements are required to distinguish the effect of CT interaction on the radiative (k pT) and radiationless (kGT) TI - So transitions, as has been done for the heavy-atom effect (Tables 6.4, 6.5 and 9.13). Christodouleas and McGlynn l9 have studied the I(DA)*-3(DA)* intersystem crossing process in DA complexes of naphthalene with TNB, TCPA, TBPA and TIPA (tetraiodophthalic anhydride) in rigid etherisopentane solutions at 7rK. They compared the ratio 10D taking a = 5 A. The reaction kinetics of exciplex formation (9.60) are analogous to those of excimer formation (7.2). The excimer relations of Chapter 7 are directly applicable to exciplexes formed by iM* (:=A*) with the following simple substitutions: (a) suffix E (exciplex) for suffix D (excimer); (b) [D] (donor concentration) for [1M]; (c) [lE*] (exciplex concentration) for [lD*] (excimer concentration); and (d) [D]h (donor half-value concentration at which ([>FM = -!qFM, ([>FE = tqFE) for [lM]h.

9.8 Fluorescence of Exciplexes

429

Knibbe et al. 46 observed the fluorescence lifetime 7"E and quantum yield FE of the anthracene-DE A exciplex in a range of solvents of different dielectric constant E. 7"E was measured in solutions containing 10- 4 M anthracene and > 0·1 M DEA, which reduced FM to FE) corresponds to a decrease of kFE TE (= kFE/kE)' The results (Figure 9.8) show that kIE' the internal quenching rate of the exciplex, increases, and kFE> its radiative transition probability, decreases, with increase in the solvent E. Mataga and co-workers 50 - 51 have made similar studies of the AD exciplexes of aromatic hydrocarbons with DMA and related donor molecules. Table 9.18 lists their observations of the exciplex fluorescence spectra51 and of the fluorescence quantum yields, lifetimes and rate parameters of pyrene and the pyrene-DMA exciplex in various solvents. The scatter in the kFM values somewhat limits the reliability of the experimental data, but they observe a significant decrease in the exciplex radiative transition probability, kFE' and an increase in its radiationless transition probability, kIE' with increasing solvent E. These results, which confirm those of Weller and co-workers,45-46 will be discussed in §9.9. Chandross and Ferguson 37 have studied the fluorescence spectra of the DA exciplexes of various aromatic hydrocarbons with 9-cyanoanthracene (CNA) or 9,1O-dicyanoanthracene (DiCNA) as acceptor. A standard solution of the acceptor in methylcyclohexane was excited in its 0 - 0 absorption band, and the fluorescence spectra were measured for various concentrations of added donor. DA exciplex fluorescence was observed when hexamethylbenzene, 2,3-dimethylnaphthalene, 2-methoxynaphthalene, phenanthrene or pyrene was added to CNA or DiCNA, and when

9.8 Fluorescence of Exciplexes

431

naphthalene was added to DiCNA, but not to CNA. The addition of 9-methylanthracene quenched the CNA and DiCNA fluorescence, but no exciplex fluorescence was recorded. Figure 9.9 shows the effect of 0.1 M additions of naphthalene, phenanthrene, hexamethylbenzene, 2,3-dimethylnaphthalene and pyrene on the fluorescence spectrum of a 7·6 x 10-5 M solution of 9,1O-dicyanoanthracene. 37 An approximate linear relation

c

OJ

24 x 10 3

23

22

2!

20

19

18

17

Wavenumber (cm- 1)

Figure 9.9 Exciplex fluorescence. Fluorescence spectra of 7·6 x 10- 5 M solution of 9,1O-dicyanoanthracene in methylcyc/ohexane: a, alone, and with the following addi-

tions: b, 0·1 M naphthalene; c, 0·1 M phenanthrene; d, 0·1 M hexamethylbenzene; e, 0·1 M 2,3-dimethylnaphthalene; and f, 0'1 M pyrene (after Chand ross and Ferguson 3 ?) between Em and the oxidation potential of the aromatic donor, which is linearly related to 1D , was observed, confirming the CT nature of the DA exciplex. Table 9.16 lists the fluorescent exciplexes of the aromatic hydrocarbons that have been observed, apart from excimers (Chapter 7) and mixed excimers (Table 9.15). The aromatic hydrocarbon exciplexes appear generally to be of 1: 1 stoichiometry. Walker et al. 27 have studied exciplex formation by the heterocyclic compound, indole,

(X) H

Molecular Complexes and Exciplexes 9.8

432

and its derivatives with polar solvents, and they have reported 1 : 2 and I : I solute-solvent stoichiometry with associating and nonassociating solvents, respectively. The solute molecule M has a characteristic structured molecular fluorescence spectrum (0 - 0 transition = Mo) in non-polar solvents, but in polar solvents a structureless fluorescence band (peak = Em) characteristic of the exciplex is observed. In a mixed non-polar/polar solvent system both emissions occur, and the ratio oftheir intensities changes with solvent composition, consistent with the following process, (9.70)

where S represents the polar solvent molecule, and (MS n )* (== E*) the fluorescent exciplex. We define kFM' kFEas the fluorescence rate parameters and kIM, klE as the internal quenching rate parameters of M * and E*, respectively, and kEM [s]n and kME as the rates of E* formation and dissociation, respectively. The ratio of the quantum yields of E* and M* fluorescence is given by cJ>FE cJ>FM

kFE[E*] kFM[M*] kFE kEM[s]n = K [S]D J kFM(kFE + kJE + k ME )

(9.71)

Double-logarithmic plots of (cJ>FE/cJ>FM) against [S], where [S] is the polar solvent monomer concentration determined from infra-red studies, are linear and of gradient 11. When S is a polar, associating solvent (methanol, n-butanol) it is found that n = 2, i.e. 1: 2 exciplexes are formed. When S is a polar, non-associating solvent (acetonitrile, p-dioxan, diethyl ether) n = ], i.e. 1: 1 exciplexes are formed. The properties of the fluorescent exciplexes of indole and its derivatives 27 are summarized in Table 9.19. The values of (Mo - Em) are listed, where Mo is observed in a non-polar solvent (n-pentane, cyclohexane) and Em is the peak of the exciplex fluorescence band in the pure polar solvent. (9.71a) where E:'" is the energy of the exciplex in its zero-point vibrational state, Rm is the ground-state repulsive energy in the equilibrium exciplex configuration, and N is the non-specific dielectric shift of Em due to the change in polarity of the solvent (§4.12). The values of (E:'" + Rm) in Table 9.19 were obtained by subtraction of the monomer emission spectrum from a composite M* + E* emission spectrum in a mixed solvent. Longworth 9 0 has confirmed exciplex formation between 1, 2-dimethylindole (M) and isopropanol (S) in 3-methylpentane solutions at room

9.9 Impurity Quenching of Fluorescence

433 4

temperature. The addition of [S] up to 0·1 M to [M] = 10- M solutions causes no change in the absorption spectrum, but the fluorescence spectra exhibit a progressive red-shift and an iso-emissive point (fluorescence intensity independent of [S]) at ,\ = 326 nm. The latter implies a twocomponent (M *, E*) equilibrium, which in this case corresponds to 1: 1 exciplex stoichiometry. Drying of the isopropanol was essential to obtain reproducible results, and the 1:2 exciplexes reported by Walker et al. 27 were not confirmed. Indole is an analogue of the aromatic amino-acid, tryptophan. Longworth 90 observed a red-shift in the fluorescence spectrum of the denatured enzyme, ribonuclease Tj, on the addition of urea, which he attributed to a tryptophanyl exciplex (see p. 632). AD exciplexes can also be produced by the interaction of (solvated) aromatic anions (As) and donor cations (Dt). Weller and Zachariasse 95 compared the chemiluminescence spectrum, produced when an ether solution of As is added slowly to crystalline Wurster's Blue perchlorate, which contains stable cations (D+), with the fluorescence spectrum of the final products (A, D) of the electron transfer reaction. Three types of behaviour are observed: (i) with A = anthracene, the chemiluminescence emitter (CLE) = 1A *; (ii) with A = 2,4,6-trimethylbenzonitrile, CLE = ID*; and (iii) with A = naphthalene, biphenyl, p-methylbiphenyl or p,p'-dimethylbiphenyl, CLE = IA*, ID* and I(A-D+). Thermodynamic considerations show that the primary excited species are (i) 3A *, (ii) 3D*, and (iii) 3A * and 3D*, respectively. The chemiluminescence originates from (i) 3A * - 3A * interaction, yielding 1A * (+ 1A), (ii) 3D* - 3D* interaction, yielding ID* (+ ID), and (iii) 3A* - 3A*, 3D* - 3D* and 3A * - 3D* interactions, the last process corresponding to the heteropolar triplet-triplet association process, (9.72) 9.9 Impurity quenching of fluorescence Excimer formation accounts satisfactorily for the concentration quenching of the fluorescence of the excited singlet state 1M* of an aromatic hydrocarbon molecule by the diffusion-controlled interaction with a groundstate molecule 1M of the same species (Chapter 7). In a similar manner exciplex or excited DA complex formation may explain the impurity quenching of the 1M* fluorescence by interaction with a ground-state molecule Q of a different species. The role of excited complex formation in impurity quenching has been shown by various studies. Leonhardt and Weller 44 observed the quenching

434

Molecular Complexes and Exciplexes 9.9

of the fluorescence of acridine by amines. Table 9.20 presents their measurements of the Stern-Volmer impurity quenching coefficient, kQM TM , of the acridine fluorescence as a function of the quencher ionization potential I Q • The sum of the diffusion coefficients of M(D M ) and Q(DQ), and the encounter parameter, pR, evaluated from the relation (7.55) for a diffusion-controlled process, are also listed. The quenching rate kQM and the encounter parameter pR increase markedly with decrease in the ionization potential IQ of the quencher, which acts as the donor in the formation of the AD exciplex responsible for the quenching. Klein 56 has made similar studies of the effect of the ionization potential or electron affinity of M or Q on the impurity quenching rate parameter kQM for alkyl benzene solvents and scintillator solutes with various quenchers. Table 9.21 lists his measurements of the quencher reduction potential E t , which is linearly related to the quencher electron affinity A Q , and of kQM for liquid toluene to which the quencher is added. In this case Q acts as the acceptor in the formation of excited DA complexes orexciplexes and kQM increases with increase in AQ. Earlier studies of the impurity quenching offluorescence in fluid solutions as a function of solvent viscosity57 - 58 identified two quenching processes: (a) a viscosity-independent process, referred to as static quenching; and (b) a diffusion-controlled process, referred to as dynamic quenching. When the quenching involves a collisional encounter between IM* and Q, a reasonable distinction can be made between static and dynamic quenching. Static quenching is attributed to bound or contact DA complexes, present in the ground state, which compete with 1 M for the incident excitation, and which yield excited DA complexes (and quenching) directly by absorption. Dynamic quenching is due to excited complexes or exciplexes formed by diffusion-controlled encounters of I M* and Q, subsequent to the excitation of 1 M *. The distinction between static and dynamic quenching is less clear cut when the interaction distance, Ro , between 1 M* and Q exceeds their encounter separation R. This occurs when the quenching is due to either (i) Coulombic (e.g. dipole-dipole) interaction , leading to energy transfer from IM* to lQ* , or (ii) electron-exchange interaction between 1 M* and Q.

The influence of diffusion on Coulombic energy transfer (i) is discussed in §11.10. The present discussion of impurity quenching will be restricted to systems in which 1M * is lower in energy than lQ* , in order to exclude process (i). However, electron-exchange interaction (ii) plays an important

9.9 Impurity Quenching of Fluorescence

435

role in many impurity quenching processes and it cannot therefore be omitted. In discussing impurity quenching, the term 'exciplex' will be extended to include all M* + Q) entities which interact, either collisionally or by electron-exchange interaction, without implying that I(MQ)* has a finite binding energy. The term 'contact exciplex' may be used to distinguish exciplexes with a binding energy of < kT. The kinetics of impurity quenching are considered in §9.11. Initially we shall discuss the processes

e

---:yr-- 10 ,

'M·--....-::_:- ---- -----,

/'

i (+ '0)

--

/'

/' /' ;(- 'M )

1

iv

(_'0)1(+-

/'

T I

I

i

I

I

I

vii / 3M·:...-_ _-...~ x

(_1Q )

/ 1

I I

xiii

I

3 E'

-

--

I I iX I I

--1{-;M) ____ _ .L _

~

/

·· _____ -.J /

/

~l!.....

I I I I

ii

I

•• • 1

''' I I I

I

I

I

~

/

I xi

I

I

('M

-I- 10

)

~

Figure 9.10 Schematic diagram of rate processes in exciplex formation, dissociation and quenching (Table 9.22). Solid lines, radiative processes; broken lines, radiationless processes subsequent to the formation of an excited complex, exciplex or contact exciplex. Table 9.22 and Figure 9.10 show the possible physical processes occurring in an exciplex (or excited DA complex) after its formation from 1 M* and lQ, a quencher molecule in its singlet ground state. (Quenching by oxygen and nitric oxide, which have triplet and doublet ground states, respectively, is discussed in Chapter 10). Process (v) following (i) corresponds to energy transfer from lM* to lQ*, and it is excluded if lQ* is of higher energy than 1M*. Of the remaining five processes (ii), (iii), (iv), (vi) and (vii) which compete for the I(MQ)* (= lE*) excitation, process (iv) is the only one which does not lead to the quenching of lM*. The rate parameter of quenching of lM* by lQ may be written as (9.73) 15

436

Molecular Complexes and Exciplexes 9.9

where

p= -. - kE- -kME + kE

(9.74)

is the quenching probability per encounter, and

kE

=

kFE

+ kGE + kCE + kXE

(9.75)

A recent study of perylene-DMA exciplexes in several solvents 59 has confirmed the occurrence of process (iv) by observation of the doubleexponential decay of the perylene fluorescence, which may be compared with (7.21) for the analogous case of excimer formation and dissociation. The four processes included in (9.75) are those responsible for 1M* quenching by dissipation of the 1E* excitation energy. (ii) Exciplexfluorescence (kFE) has been observed in many systems (§9.8), but it normally has a low quantum yield CPFE (=kFE/k E ), indicating that the competing radiationless processes (iii), (vi) and (vii) are more efficient. Impurity quenching commonly occurs in the absence of 1E* fluorescence. (iii) Exciplex internal conversion (kGE) to the ground state is unlikely to be efficient, because of the large energy gap. 58 This is certainly the case for isolated aromatic molecules, where intersystem crossing is the dominant internal quenching process, and the relation

(6.27) is commonly valid (§6.3). The experimental data on the pyrene excimer, discussed in §7.l6, indicate that kGE = 0 for this particular exciplex. (vii) Exciplex intersystem crossing (kXE) to the triplet exciplex state 3E* is an important quenching process in many cases. Studies of the luminescence properties of DA complexes (§9.5) have shown that kXE is considerably enhanced, relative to kTM' the corresponding 1M* intersystem crossing rate, if IQ contains heavy atoms. 3E* commonly dissociates to yield 3M* phosphorescence (x), although in a few cases 3E* phosphorescence, or dissociation yielding 3Q* phosphorescence (xi), is observed. 20 It is concluded that with heavy-atom quenchers, exciplex formation (i) followed by enhanced intersystem crossing to 3E* (vii) is the dominant mechanism of impurity quenching, as originally suggested by Kasha,60 and that 3E* normally dissociates to yield 3M* (x). Direct evidence for this is provided by the experiments of Wilkinson and co-workers,61 described in §6.2 (ii), who showed that xenon, bromo benzene and various bromide and iodide heavy-atom quenchers induce the overall process (6.21) in the aromatic hydrocarbons. They observed a correlation between the

9.9 Impurity Quenching of Fluorescence

437

decrease in the relative I M* fluorescence yield, 1>FM/(1)FM)O, due to quenching, and the increase in the relative 3M* yield, 1>TM/(1)TM)O, which was monitored by the triplet-triplet absorption. The assumption that (6.21) is the only impurity quenching process leads to the relation

(1)FM)O _ 1>FM

1

=

{1>TM(1)FM)O (1)TM)O 1>FM

I} (1)TM)O

(6.24)

Their experimental data are consistent with (6.24), and they yield values of (1)TM)O which are independent of the nature of the heavy-atom quencher Q. The results of Christodouleas and McGlynn,19 described in §9.5, show that kXE ~ 30kTM even when Q (= trinitrobenzene) contains no heavy atoms, the effect being attributed to the CT interaction . Thus the role of exciplex intersystem crossing (vii) in impurity quenching is not restricted to heavyatom quenchers. (vi) Excip/ex dissociation into ions (k CE ), or direct electron transfer between I M* and I Q, has been proposed by Baur62 and Weiss 63 to account for impurity quenching. Leonhardt and Weller 30 ,44 have made flashspectroscopic studies of deoxygenated 10- 4 M solutions of perylene containing a sufficient concentration (0·05 to 0·8 M) of quencher to give at least 80 % quenching. With an amine quencher (triethylamine, aniline, DMA, DEA) in a polar solvent (acetonitrile, dimethylformamide) they observed two distinct components in the transient absorption spectra : a sharp band at 580 nm due to the perylene mono negative ion, 2M-; and a structured spectrum, with a maximum at 490 nm, due to perylene in its excited triplet state, 3M*. Figure 9.11 shows the transient absorption spectra of perylene + 0·15 M DMA in acetonitrile. 44 With an amine quencher in a non-polar solvent (benzene, methylcyclohexane) only the 3M* absorption is observed, and its intensity is about twice that in the polar solutions. With sodium iodide, i.e. the iodide ion 1-, as the quencher only the 3M* absorption occurs, even in polar solvents, showing that with a heavy-atom quencher the intersystem crossing process (vii) dominates. Table 9.23 lists the percentages of the two products 2M- and 3M*, estimated from the transient absorption spectra, for various solutions. 30 The sum of the diffusion coefficients (DM + DQ), the quenching-rate parameter, k QM , and the encounter parameter, pR, evaluated from (7.55) for a diffusion-controlled process, are also listed. 30, 44 The impurity quenching in polar solvents differs from that in non-polar solvents, where it can be simply explained by exciplex intersystem crossing (vii). The magnitude of pR in the polar solvents (Table 9.23) indicates that the primary quenching process occurs at an encounter distance R > 7 A (since p.;:; 1), which is twice the intermolecular separation in excimers and

438

Molecular Complexes and Exciplexes 9.9 DA complexes. Leonhardt and Weller 30 conclude that in polar solvents quenching can occur through electron transfer without 1 M and 1 Q* forming a sandwich-type complex. They postulate a solvent-shared ion pair Ms'" Qt, in which the radical ions are partially solvated, as the primary intermediate in the quenching process in polar solvents. The solvated exciplex may dissociate into ions (ii), it may undergo intersystem crossing (vii) and dissociate yielding 3M* (x), or it may undergo spontaneous reversal of the electron transfer to yield molecules in their ground and/or triplet states. 60r:0'--_ _-=-50r:0'----- -...:..:r'------r-;r-;.:; 4 ·5 r--=p -fl

fl p+

l"

d

1\

•t

I •

~

I

t

it

t \

i

1·5

.'

•

c

Q

~

j \.

!",\ p T

'.", /

.~

V",

\

9 ~5---~~/--2LO--_-_-~\L---~--~S£~~±d 11-+ ( kK)

Figure 9.11 Transient absorption spectrum of perylene + 0·15 M dimethyl aniline in acetonitrile. P- , absorption spectrum ofperylene mononegative ion; P, absorption spectrum of perylene; pT, absorption spectrum of triplet perylene (right-hand ordinate); A, absorption of filter solution (right-hand ordinate) (after Leonhardt and Weller 44 )

The fluorescence properties of anthracene-DEA exciplexes (Figure 9.8) and pyrene-DMA exciplexes (Table 9.18) show that the exciplex radiative transition probability, kFE' decreases and its radiationless transition probability, kIE' increases with increase in solvent dielectric constant, i.e. with increase in the solvent-shared ion-pair character ofthe exciplex. From (9.48), neglecting the small term in ifi2 (M +Q-), the exciplex wavefunction may be written as (9.76) and the radiative transition moment to the (dissociated) ground state ifio (MQ) is (9.77) Mataga et al.53 explain the decrease in solvent polarity, by proposing that

kFE

(IX IMEOI2) with increase in

9.10 Photochemical Quenching of Fluorescence

439

decreases with increase in polarity, due to the increased M-Q+ separation, which reduces their overlap integral: (ii) > ; (iii) IX increases and y and 0 decrease with increase in polarity. (i)

Postulate (i) is implicit in the Mulliken theory3 of DA complexes (9 .27), and (ii) is similar to the Murrell modeP8 of contact CT absorption (§9.4). From the solvent spectral shifts (Tables 9.17, 9.18) the AD exciplexes appear to be predominantly of CT character, i.e. IX ;l> y, o. If this is the case, postulates (ii) and (iii) of the Mataga model may be redundant (see p. 632). 9.10 Photochemical quenching of fluorescence

In addition to the photophysical processes listed in Table 9.22, exciplex formation can lead to a photochemical reaction. The two components of the exciplex may associate to form a stable molecule, such as the photodimers of anthracene and its derivatives (§7.10). Alternatively, the exciplex may dissociate yielding products differing from the original reactants. A full discussion of such photosensitized chemical reactions is beyond the scope of this book. The quenching of the fluorescence of aromatic hydrocarbons by carbon tetrachloride will be considered to illustrate the role of such reactions. When a solution of anthracene (A) in carbon tetrachloride (CCI 4 ) is exposed over a period to 365 nm radiation, which is absorbed only by the anthracene, the characteristic absorption spectrum of the hydrocarbon fades almost entirely, showing that a photoreaction occurs, resulting in the loss of the anthracenic structure. In the presence of dissolved air, photooxidation also occurs. Bowen and Rohatgi 64 have made a kinetic study of the behaviour. The photochemical process in oxygen-free solutions is explained as the primary formation of radicals (9.78)

which removes J A * with a quantum efficiency of qRM = 0·4. This is followed by dimerization of ·ACl and further combinations of the radicals to give substitution products of dihydroanthracene which lose HCI on standing or heating. The J A * fluorescence quantum yield (- 00 . Kallmann-Oster 65 evaluated TMkOM from measurements of qFM/ ifJFM against [Q] and (4.31), and from measurements of ifJRM/qRM against [Q] and (9.79), and obtained similar values by the two methods. The results confirm the kinetic scheme, and they show that free radical formation is one of the products of the exciplex, responsible for the impurity quenching. They do not prove it to be the only one, as assumed by Kallmann-Oster. The results of Table 9.24 show that qRM = 0·4 for anthracene, and qRM = 0·15 for 9,1O-diphenylanthracene, two of the compounds which she studied. Klein 56 has investigated the relation between free radical formation and fluorescence quenching for deoxygenated solutions of CCl 4 in benzene, toluene, p-xylene and mesitylene. He concludes that the fluorescence quenching is due to exciplex formation, and that free radicals are one of the exciplex products. He obtains values of qRM = 0·55 for benzene, 0·85 for toluene, 0·9 for p-xylene and 0·8 for mesitylene.

441

9.11 Kinetics of Impurity Quenching

Bowen and Sahu 66 have measured the CCl 4 quenching parameter, TM k QM , for anthracene and ten of its derivatives in six different solvents. The fluorescence of 9-cyanoanthracene, which has a high electron affinity, is not quenched by CCI 4 • This suggests that the other anthracene derivatives act as donors in forming DA exciplexes with CCI 4 , and that such exciplex formation is a prerequisite for quenching. 9.11 Kinetics of impurity quenching The impurity quenching of fluorescence has been studied over the last half-century, and several empirical and theoretical relations have been proposed to describe the observed behaviour. Forster 58 has given an excellent account of the evolution of the subject up till 1950, and only a brief outline of the historical development will be presented here to introduce the concepts involved. In 1919 Stern and Volmer67 obtained the relation (9.80) 1 + k[Q] for fluorescence quenching in the gas phase. In 1929 Vavilov 68 applied it to dynamic quenching in fluid solutions, and this was followed by most other workers in the field. In 1924 Perrin,69 in discussing concentration quenching, introduced the concept of the 'active sphere', a volume of interaction around a quencher molecule such that a fluorescent molecule excited within this volume is quenched instantaneously, while fluorescent molecules excited outside this volume are unquenched. This provides a model of static quenching which does not require the formation of a bound complex between M and Q in the ground state. If v is the volume (in cm 3) of the active sphere of each quencher molecule and n = [Q] N x 10-3 is the number of quencher moleculesin unit volume V(=l cm 3 ), the probability that a fluorescent molecule M will lie within an active sphere is p = e- nv / v (9.81)

Hence on excitation the static quenching of the fluorescence is kME and hence kQM = kEM' i.e. the dynamic quenching is diffusion-controlled. CBr 4 , O 2 and S02 exhibit this 3 on

o

Q

:':: 100 c

"

o

.'!' u .;:

Q 2 C

- 1'5 - 1,4 - 0,54 -0,36 ;;>-1'3 ;;>-1,2 ;;>-0·9 ;;>-0'4 ;;>-1·1 ;;>- 0,8 -0,38 - 0,246 -0·20 - 0'14 -0,08 0·65 0·67 0·147 0-42 0·49 0'552 0'58 0·61 0·64 1·19 1'38 -0,20 - 0'06 0·014 0·17 0·20 0·25 0·308 0·69 0·39 0'417 0·55 0'57 0'579 0·68 1-16

Th. Th. Th. ES Th. KE KE ES ES ES ES ES ES Th. Th. Th. Th. Th. KE KE Th. EQ Th. EQ Th. Th. Th. KE KE Th. Th. Th. Th. EQ Th. EQ KE EQ Th. Th. Th. EQ Th. KE

a b c d e, f e g d d d d d d a b

f e c h g b i a c f e h g a e b c i f j

h i b f c a g

Molecular Complexes and Exciplexes

463

Table 9.6 (continued) Compound

Code 4.2

Tetracene

4.3

1 : 2-Benzanthracene

4.4

4.5

4.6

Chrysene

3:4-Benzophenanthrene

Triphenylene

5.1

Perylene

5.2 5.3 5.4

1 :2-Benzopyrene 3: 4-Benzopyrene Pentaeene

5.6

1: 2: 3 :4-Dibenzanthraeene

5.7

1: 2 : 5: 6-Dibenzanthraeene

5.8

1: 2 : 7 : 8-Dibenzanthraeene

5.9

Pieene

5.14 5.15

3 :4 : 5 : 6-Dibenzophenanthrene Pentaphene

6.2

1: 12-Benzoperylene

6.10 6.14 6.17

1 : 2 : 7 : 8-Dibenzotetraeene 1 :2:3:4-Dibenzopyrene 1 :2:4 : 5-Dibenzopyrene

A (eV)

Method

Ref.

0·82 0·95 0·46 0·61 0·62 0·696 0·04 0·313 0·33 0·419 0·47 - 0·14 0·33 0·37 0·542 -0·28 - 0·033 0·12 0·14 0·284 0·727 0·80 0·88 0·41 0·676 1·01 1·035 1·19 0·446 0·58 0.501 0·65 0·463 0·62 0·75 0·442 0·59 0·52 0·63 0·73 0·50 0·573 0·73 0·75 0·683 0·59

Th. Th.

a c

EO

i

Th. Th.

c a

EO

j

Th. Th.

a b

EO EO Th. Th.

c a

EO

i

Th.

e

EO

j

Th. Th. Th.

a b e

EO EO

j

Th. Th. Th. Th . Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th. Th.

b a e b b a b e b e b a,e b e a b e e a e a b e a b b

Molecular Complexes and Exciplexes

464

Table 9.6 (continued) Compound

Code

7.1

Coronene

A

Biphenyl

C G J L M

Biphenylene Azulene m-Terphenyl o-Terphenyl trans-Stilbene Graphite

A (eV)

0·18 0·385 0'54 -0,78 - 0,37 - 0·29 0·41 0·70 0·42 0·052 0'587 - 0'51 - 0,35 1-33 3·87 4·23 4·39

Method Th. Th. Th . Th. Th. Th.

KE KE Th. Th.

Ref. a b

e a e b h g

e b

EQ Th. Th.

KE Th. Th.

EQ

a a g a e I

References

a. R. M. Hedges and F. A. Matsen, J. Chern. Phys., 28, 950 (1958). b. S. Ehrenson, J. Phys. Chern., 66, 706, 712 (1961). c. D. R. Scott and R. S. Becker, J. Phys. Chern., 66, 2713 (1962). d. R. N . Compton, L. G . Christophorou and R. H. Huebner, Phys. Lett., 23, 656 (1966). e. N. S. Hush and J. A. Pople, Trans. Faraday Soc. , 51, 600 (1955). f. J. R . Hoyland and L. Goodman, J. Chern. Phys., 36, 21 (1962). g. L. E. Lyons, Nature, 166, 193 (1950). h. BJackredge and Hush, quoted in ref. e. i. W. E. Wentworth and R. S. Becker,J. Arn. Chern. Soc., 84, 4263 (1962). j. W. E. Wentworth, E. Chen ane! J. E. Lovelock, J. Phys. Chern., 70, 445 (1966).

~ S. ~

Table 9.7 Binding energy (B) of DA complexes of aromatic molecules with various acceptors

n

Iodine . -_ _- J >

Code

Compound Benzene

IA IB

IC 1D IE IK

IF

2

Toluene o-Xylene m-Xylene p-Xylene Mesitylene Durene Hexamethylbenzene 1,3,5-Triethylbenzene Hexaethylbenzene 1,3,5-Tri-t-butylbenzene ChI oro benzene 0- Dichlorobenzene Naphthalene

B(eV)

Solvent

0·056 0·056 0·078

CCI 4 n-Hexane n-Hexane

0·087 0·094 0·124 0·120 0·162 0·114 0·077 0·094 0·048 0·046 0·060 0·067 0·071 0·071 0·071 0·078

n-Hexane CCI. CCl 4 CCl 4 CCl 4 CCl 4 CCl 4 CCl 4 n-Hexane n-Hexane n-Heptane Cyclohexane n-Hexane Chloroform CCl 4 n-Hexane

Ref. a b b

p-Chloranil '-----. B(eV) Solvent Ref. 0·071

CCI 4

c

1,3,5-Trinitrobenzene B(eV)

Solvent

Ref.

0·074 0·019 0·076 0·037

CCI 4 CHCI 3 CCI 4 CHCl 3

d e d e

b a a a a a a a b b g g

0·191 0·231

CCl 4 CCl 4

c f

0·121

CCl 4

e

0·094 0·049 0·053 0·174 0·204

CCI 4 CHCh CHCI 3 CCl 4 CCl 4

d e e d d

0·186 0·095

CCl 4 CHCI 3

d e

~ ... ~

I

~

~

!l I>l

=

Q.

tr:I ~

n

~ ~ ~ ~

'"

g

g g

b

"'8l"

~

0'1

Table 9.7 (continued)

p-Chloranil

Iodine

'-------,

Code

Compound

2A

1- Methylnaphthalene

2B

2-Methylnaphthalene

B(eV)

Solvent

0·091 0·091 0·091 0·091

n-Rexane CCl 4 n-Rexane CCl 4

Ref.

B(eV)

Solvent

Ref.

b h

0·104

CRC!3

e

b

0·111

CRC!3

e

0·104 0·129 0·130 0·119 0'187 0·114

CRC!3 CRC!3 CRC!3 CRCl 3 CC!4 CRCI 3

e e e e

a:S2.

C

n c

h

3.1 3.2

Acenaphthene I-Naphthylamine 2-Naphthylamine Anthracene Phenanthrene

0·141 0·158

CCl 4 CC!4

c c

4.1 4.3 4.6 A M

Pyrene 1: 2-Benzanthracene Triphenylene Biphenyl trans-Stilbene

0·141 0·154 0·162 0·093 0·139

CCl 4 CCl 4 CCl 4 CCl 4 CCl 4

c c c c c

2Z

1,3,5-Trinitrobenzene ' - - - - -, B(eV) Solvent Ref.

fI>

e

...5' ("'J Q

e

"5!. fI> ~

fI>

VI ~

:I

=-t'i

~

n

'§: fI>

~

fI>

VI

Molecular Complexes and Exciplexes

467

References

a. b. c. d. e. f. g. h.

R. M. Keefer and L. J . Andrews, J. Am. Chem. Soc., 77, 2164 (1955). J. A. A. Ketelaar, J . Phys. Rad., 15, 197 (1954). G. Briegleb, Elektronen-Donator-Acceptor-Komplexe, Springer-Verlag, Berlin, 1961. G. Briegleb and J . Czekalla, Z . Elektrochem., 59,184 (1955). A. Bier, Rec. Trav. Pays-Bas, 75, 866 (1956). G. Briegleb and J. CzekalIa, Z. Elektrochem., 58, 249 (1954). P. A. D. de Maine and J. Peone, J. Mol. Spectr., 4, 262 (1960). P. A. D. de Maine, J. Chem . Phys., 26, 1192 (1957).

16

Molecular Complexes and Exciplexes

468

Table 9.8 Fluorescence lifetimes (in ns) of crystal DA complexes of aromatic hydrocarbons with TNB and TCPA at 293°K and 77°K22 TNB Code

Donor

IF 1K 2 3.1 3.2 4.3

Hexamethylbenzene Durene Naphthalene Anthracene Phenanthrene 1 :2-Benzanthracene

TCPA

2·6 3-6 5·0 3·6

7·7 8'1 2·6 4·3 3·0 7·3

11'0 6·8 2'3

Molecular Complexes and Exciplexes

469

Table 9.9 DA complexes of aromatic hydrocarbons in solution at 77°K. Absorption maximum (va), fluorescence maximum (vr) and mirror-symmetry wavenumber (v o) in 10 2 cm- i (ref. 23) Code

Donor

lK

Durene

2

Naphthalene

3.1

Anthracene

3.2

Phenanthrene

4.3

1: 2-Benzanthracene

Acceptor

Va

vr

Vo

p-Chloranil 2,5-Dichloroquinone 1,3,5-Trinitrobenzene TCPA p-Chloranil 2,5-Dichloroquinone 1,3,5-Trinitrobenzene TCPA 1,3,5-Trinitrobenzene TCPA

206 227 280 294 207 224 265 278 216 235 214 235 268 285 170 224 237

150 163 195 217 156 173 195 225 164 190 148 158 192 215 135 170 196

180 193 229

p-Chloranil

2,5-Dichloroquinone 1,3,5-Trinitrobenzene TCPA p-Chloranil 1,3,5-Trinitrobenzene TCPA

179 195 227 250 187 209 174 192 220 241 151 194 216

Molecular Complexes and Exciplexes

470

Table 9.10 Phosphorescence spectra of DA complexes of aromatic hydrocarbons in rigid glass solutions at 77°K (energies in 10 2 em- I)

Code

Donor

(ET)o

1 .1A 1E

Benzene Toluene Mesitylene

295 288 280

1K

Durene

279

IF

Hexamethyl~

274

benzene 2

3.1 3.2

4.3 4.6

Naphthalene

Anthracene Phenanthrene

1: 2-Benzanthracene Triphenylene

213

149 217

167 238

Acceptor (ET)A TCNB TCNB TCNB PMDA TCPA PA TCNB PMDA TCPA TCPA TCPA (crystal) PA TCNB PMDA TCPA PA TCNB TCPA TCPA (crystal) TBPA TIPA TNB TCNB TNB TCPA TCPA (crystal) TBPA TNB TCPA TCNB

226·5 226·5 226'5 223 235 258 226'5 223 235 235 258 226·5 223 235 258 226·5 235

(vp)max

~220

207 205 198 200 202 227 195 203 200 197 196

A A DA DA DA DA DA DA DA DA DA

224 183 198 202 209 198

DA DA DA DA DA D D D

~217

213 213 190 212 213 150·6

226·5 235

235 226·5

Assignment (VF)m .. Ref.

(vp)o

192 217 215 199 215'5 195 183 212 167 168 193

263 247 225 225 2.15 215 215 210 217 197 200 198 223 250 239

D D D DA D D D D

174 202 196 241

D D D DA

216 194

228

~196

a a a a a a a a a b b a a a a a a b b c c d,c a c b c b c b b a

Acceptors: TNB, 1,3,5-trinitrobenzene; TCNB, 1,2,4,5-tetracyanobenzene; PMDA, pyromellitic dianhydride; TCPA, tetrach lorophthalic anhydride; PA, phthalic anhydride; TBPA, tetrabromophthalic anhydride ; TIPA , tetraiodophthalic anhydride. References a. S. Iwata, J. Tanaka and S. Nagakura, J. Chem. Phys., 47, 2203 (1967). b. J. Czekalla, G. Briegleb, W. Herre and H. J. Vahlensieck, Z. Elektrochem., 63, 715 (1959). c. N . Christodouleas and S. P. McGlynn, J . Chem. Phys., 40,166 (1964). d. S. P. McGlynn, J. D. Boggus and E. Elder, J . Chem . Phys., 32, 357 (1960).

Molecular Complexes and Exciplexes

471

Table 9.11 Phosphorescence lifetimes (s) of aromatic donors (TT)O in solution

and of solution and crystal DA complexes at 77°K 5 (solvent : 3: 1 n-propylether-isopentane) DCPA

TCPA

TBPA

,.-------"----

~

~

Code

Donor

(-TT)O

Soln.

Cryst.

Soln.

Cryst.

Soln.

Cryst.

IF

Hexamethylbenzene Durene Naphthalene Anthracene Phenanthrene 1 :2-Benzanthracene Coronene

5·6

0·095

0·018

0·0085

0·0011

0·0047

0·001

5·9 2·4 0·09 3·6 0·40

0·35 2·1

0·26 0·049

0·002 0-45

0·0095 0·29

0·0012 0·029

3·0

0-41

0·25 1·6 0·04 1·8 0·41

0·25

0·36

0·019

5·1

0·86

IK 2 3.1 3.2 4.3 7.1

9·3

1·05

0·16

Molecular Complexes and Exciplexes

472

Table 9.12 Phosphorescence lifetimes of protonated and deuterated hydrocarbons and their DA complexes in hydrocarbon glass solutions at 77°K26 Code

Donor

2.d

Naphthalene'd B

2

Naphthalene'h B

3.2d

Phenanthrene'd 10

3.2

Phenanthrene' h 10

'f From (9.47).

(TT)O

21 2·4 15 3·7

Acceptor

TT

observed

TCPA TBPA

4·2 0·39

TCPA TBPA

1·5 0·29

TCPA TBPA

2·6 0·40

TCPA TBPA

1·6 0·34

TT

calculatedt

1-6

0·34

1·7 0·37

473

Molecular Complexes and Exciplexes

Table 9.13 Rate parameters (in S- I) of radiative and radiationless TI - So transitions in aromatic hydrocarbons and their DA complexes, from data of Table 9.12 TCPA complex TBPA complex

D onor

,------A-------

Code

Donor

(kT)o (kGT)o (kpT)o

kT

kGT

kPT

,------A-------

kT

kGT

kPT

2

Naphthalene·h g

0·42

0·39

0·03

0'67 0·45 0·22 3·45 0·93 2·52

2d

Naphthalene'd g

0·05

0·02

0·03

0·24 0·02 0·22 2·56 0'04 2'52

3.2

Phenanthrene'h lo 0'27

0'24

0·03

0·63 0·28 0·35 2·94 0'52 2·42

3.2d Phenanthrene'd lo 0·07

0·04

0·03

0·39 0'04 0·35 2·50 0'08 2'42

474

Molecular Complexes and Exciplexes Table 9.14 Phosphorescence lifetimes (s) of donors (TT)O, acceptors (TT)A, and DA complexes (TT)OA, in EP solutions at 77°K20 Code

Donor

(TT)O

Acceptor

(TT)A

(TT)OA

lK

Durene Durene

5·9 5·9

TCNB PA

3·2 1·4

1·9 0·78

IF

Hexamethylbenzene Hexamethylbenzene

5·6 5·6

TCNB PA

3·2

0'41 0·3

1-4

Molecular Complexes and Exciplexes

475

Table 9.15 Mixed excimers of aromatic compounds Notes Phenyl Phenyl Anthracene 9,1O-Dimethylanthracene 9, 1O-Di-n-propylanthracene (DPA) DPA DPA DPA DPA DPA Pyrene Pyrene I-Methylpyrene 1: 2-Benzanthracene

o-Tolyl

Ref.

Intramolecular (Cpd. 15, Table 7.7) m-Tolyl Intramolecular (Cpd. 14, Table 7.7) 9,10-Dichloroanthracene Sandwich dimer in rigid glass Anthracene Room-temperature solution

37, 38 34

Anthracene

34

Room-temperature solution

9-Methylanthracene Solution, .tJHE = -4,6 kcal/mole 9-n-Propylanthracene Solution, .tJHE = -5,0 kcal/mole l-a-Oxyethylanthracene Solution, .tJHE = -5,3 kcal/mole 9-a-Oxyethylanthracene Solution, .tJHE = -4,6 kcal/mole 9-Acetoxyanthracene Solution, .tJHE = -4'4 kcal/mole I-Methylpyrene Room-temperature solution 4-Methylpyrene Room-temperature solution 4-Methylpyrene Room-temperature solution Room-temperature solution 6-Methyl-l: 2-benzanthracene 5-Methyl-l : 2-benz- 6-Methyl-l: 2-benzRoom-temperature solution anthracene anthracene

36 36

35 35 35 35 35 29 43 29 29 29

Molecular Complexes and Exciplexes

476

Table 9.16 Fluorescent exciplexes of aromatic hydrocarbons

Code

Hydrocarbon

Other compound

Solvent

Methyicyclohexane Hexamethylbenzene CNA Methyicyclohexane DiCNA p-C6 H.(COOCH 3 )2 Methylcyclohexane 1K Durene (for other solvents, see Table 9.17) Methyicyclohexane Naphthalene DiCNA 2 DEA DEA Triethylamine Triethylamine 2,3-DimethylCNA Methylcyclohexane 2E naphthalene DiCNA Methyicyclohexane Methyicyclohexane 2-MethoxyCNA 2Y naphthalene Methyicyclohexane DiCNA DEA Methyicyclohexane 3.1 Anthracene DEA (for other DEA solvents, see Table 9.17) DMA Cyclohexane DMA DMA Triethylamine Triethylamine 3.1B 9,1O-DimethylAcridine Toluene anthracene Acridine Toluene 3.1F 9, 1O-Di-n-propylanthracene Acridine 3.lH 9,1O-DichloroToluene anthracene 3.2 Phenanthrene DEA DEA Pyrene DEA Methylcyclohexane 4.1 DEA DEA (for other solvents, see Table 9.17) n-Hexane (for DMA other solvents, see Table 9.18) DMA Cyclohexane DMA DMA p-C6 H.(CN)2 Toluene (for other solvents, see Table 9.17) 4.2 DEA DEA Tetracene 1:2-Benzanthracene DEA 4.3 DEA DMA Cyclohexane Chrysene DEA DEA 4.4 6-Ethylchrysene DMA Cyclohexane 4.6 Triphenyiene DEA DEA Cyclohexane DMA

Em (10 2 cm- I ) Ref.

208 252

31 31 45

207 234 201 220

31 47 48 31

204

31 31

IF

211 191

31 45 47

208 193 230

55 50 48 54

189

54 54

227 222 202

47 45 47

230

51

223 202 228

55 50 45

174 199 215 203 235 229 236

47 47 55 47 55 47 55

477

Molecular Complexes and Exciplexes Table 9.16 (continued)

Code

Hydrocarbon

5.1

Perylene

5.2 5.3 5.6

7.1 A

I : 2-Benzopyrene 3 : 4-Benzopyrene I: 2: 3: 4-Dibenzanthracene 1 :2: 5: 6-Dibenzanthracene 1: 2: 7:8-Dibenzanthracene Picene 3:4-Benzotetraphene I: 12-Benzoperylene I: 2: 3: 4-Dibenzopyrene Coronene Biphenyl

B D E F

Fluorene p-Terphenyl p-Quaterphenyl Fluoranthene

5.7 5.8 5.9 5.13 6.2 6.14

Other compound

Solvent

Em (10 cm- I ) Ref.

DEA DMA DMA DMA DEA DEA DEA

DEA Cyclohexane Methy1cyclohexane DMA DEA DEA DEA

184 192 191 183 198 191 201

47 55 30 50 47 47 47

DEA

DEA

202

47

DEA

DEA

206

47

DEA DEA

DEA DEA

214 195

47 47

DEA DEA

DEA DEA

192 195

47 47

DEA DEA DEA

DEA DEA Methy1cyclohexane (for other solvents, see Table 9.17) DEA DEA DEA DEA

194 231 271

47 47 45

249 215 210 188

47 47 47 47

DEA DEA DEA DEA

~ Table 9.17 Effect of solvent polarity (f - t/,) on fluorescence maximum (Em) of exciplexes 45 (energies in 10 2 em- I)

Acceptor Donor

Methylcyclohexane Toluene Diethylether Chlorobenzene Ethylacetate Dimethoxyethane H 2 CCI, H 2 CCI Acetone

Anthracenet DEA

Pyrenet DEA

p-C 6 HiCN)2 Pyrene*

p-C 6 H 4 (COOCH 3 ht Durene

Biphenyl DEAt

Pyrenet Pyrene

I-tl'

Em

Em

Em

Em

Em

Dm

0·106 0·117 0·256 0·261 0·293 0·304 0·324 0·374

211 204·5 210 197·5 192·5 188·5 187·5 186

222 213 211·5 205 200 196 196 193

228 224 212·5 212 204·5 202

252 241 243 234 229 227 224

271 254 251·5 235 229 230 229 223

210 209 210·5 210·5 210 210 210·5 210·5

217 83

230 101

246 120

279 151

210 0

(Em)o (extr.) 2fLMhca 3

257 97

~

e.. ~

n

c

;'

...

("") 0

e

'2. ~

~

~ ~

t Denotes initially excited species.

= Q..

trl ~ O. '5!.. ~

~

~

Molecular Complexes and Exciplexes

479

Table 9.18 Fluorescence properties of pyrene-DMA exciplexes in various solvents 51 ,53

Solvent

n

n-Hexane p-Xylene Benzene Toluene Chlorobenzene o-Dichlorobenzene 1,2-Dichloroethane Pyridine

1-375 1·496 1'501 1'494 1·525

E

1·89 2·27 2·28 2·38 5-62 10·2 1·448 10·36 1'507 12-30

Em (10 2 cm- I ) 230 217 215 214 209 200 193

'TM

'TE

kFM

~

kiM

kFE

klE

106 s- 1

--i>

0·73 0·66

380 130 1·9 0'7 5·0

2·6

0·83 0·41 0·23 0'53 0-45

5·9 361 130 2·3 0·5 1·8 8·1 292 110 1·4 2·0 1·0 244 120 1·0 3·4 0·54 7·8 230 98 2·3 2·1 0·57 9-6 311 47 1-4 1·8 0·32 21

qFM

q FE

0·24 0·11 0·065 0'056 0·015

(ns) (ns)

Molecular Complexes and Exciplexes

480

Table 9.19 Properties of fluorescent exciplexes of indole and derivatives 2 7

Exciplex components M*

S

Diethyl ether p-Dioxan Acetonitrile n-Butanol Methanol 1-Methylindole Diethyl ether p-Dioxan Acetonitrile n-Butanol Methanol 1,3-Dimethylindole n-Butanol Indole

N Mo-Em E~ + Rm (em-I) (em-I) (em- I)

1600 2340 3350 3930 4110 1740 2450 3220 3410 3500 3910

1600 2340 2860 2860 2960 1740 2450 2550 2550 2650 2760

~O ~O

490 1070 1150 ~O

~O

670 860 850 1150

K,

n

0·20 M - ' 0·28 M- ' 1·21 M - ' 109·2 M - 2 141·3 M - 2 0·14 M- ' 0·20 M- ' 0'78 M - ' 12·03 M- 2 9·55 M- 2 44'57 M- 2

1 1 1 2 2 1 1 1 2 2 2

Molecular Complexes and Exciplexes

481

Table 9.20 Quenching of acridine fluorescence in aqueous solution (0'03 M NaOH) at 25°C 44 DM + D Q

Quencher

(eV)

(102 cm 2 S-l)

kQMTM (M- 1)

pR (A)

NH3 CH3'NH 2 i-C 3H7'NH2 n-C 4 H 9 'NH 2 (CH 3h 'NH (CH 3h'N (C 2H s)3'N

10'16 8·97 8·72 8'71 8·24 7·82 7'56

3·10 2'35 1·80 1-65 2·00 1·80 1·45

0·38 2·45 2·4 6·5 21'5 25·2 40·1

0·012 0·10 0'13 0·39 1·07 1'40 2'75

IQ

Molecular Complexes and Exciplexes

482

Table 9.21 Quenching offtuorescence of liquid toluene S6

(10 9 M - 1 S- I)

Quencher

E-l; (volts)

Ethyl monochloroacetate Ethyl dichloroacetate Ethyl trichloroacetate

- 2-04 - 1-34 - 0-62

0-15 1-29 13-3

Allyl cyanide Allyl chloride Allyl bromide Allyl iodide

- 2-37 - 2-27 -0-72 - 0-69

< 0-01

Propyne chloride Propyne bromide

-2-04 - 0-54

< 0-01 10-8

Nitromethane Tetranitromethane

- 1-46 - 1-35

33-0 106-0

Methylthiomethane Ethyl isothiocyanate Methyldi thiomethane

- 2-6 - 2-21 -1-86

kQM

0-01 4-24 41-0

2-51 17-6 23-4

Molecular Complexes and Exciplexes

483

Table 9.22 Possible exciplex processes (see Figure 9.10)

Process (i) (ii) (iii) (iv) (v)

+ lQ

Rate

I(MQ)* I(MQ)* I(MQ)*

-->-

I(MQ)*

-->-

I(MQ)* Formation of exciplex (lE*) 1M + lQ + hVE lE* fluorescence 1M + lQ lE* internal conversion 1M* + lQ 1E* dissociation, yielding 1M* 1M + lQ* 1E* dissociation, yielding lQ*

(vi) I(MQ)* or I(MQ)* (vii) I(MQ)*

-->-

2M - -I- 2Q+}

-->-

2M+ -I- 2Q-

-->-

3(MQ)*

-->-

-->-

k pX [3E*] 1M + lQ -I- hvx 3E* phosphorescence 1M -I- lQ k GX [3E*] 3E* intersystem crossing 3M* + lQ 3E* dissociation, yielding 3M* k TX [3E*] 1M -I- 3Q* 3E* dissociation, yielding 3Q* k UX [3E*]

-->-

2M- -I- 2Q+}

-->-

2M+ -I- 2Q-

(viii) (ix) (x) (xi)

lM*

Description

3(MQ)* 3(MQ)* 3(MQ)* 3(MQ)*

(xii) 3(MQ)* or 3(MQ)*

-->-->-

-->-->-

-->-

kEMPQ]PM*] kFEPE*] kGEPE*] kME[iE*] kQE[iE*]

lE* dissociation, yielding ions

kCE[iE*]

lE* intersystem crossing, yielding triplet exciplex (3E*)

kXEPE*]

3E* dissociation, yielding ions

k CX [3E*]

Molecular Complexes and Exciplexes

484

Table 9.23 Fluorescence quenching of perylene by amines and iodide ions 30. 44

Solvent

2M- 3M* DM + D Q kQM Quencher ( %) ( %) (10- 5 cm 2 S- I) (10 9 M- 1 S-

pR I)

(A)

3·1 3·4 3·6 6·3

16·7 ]7·8 7·6 12·0

7·1 7·2

1-

1·3 ] ,4 2·6

7·9 8'0 8·0

8·0 7·6 4·0

Formamide

DMA

0·35

1·9

7'5

Methanol

DMA 1-

2·1 3·85

12·2 0·23

7'7 0·08

Benzene

DEA DMA Aniline

0 0

68 67

],8 1·9 2·]

1·2 1·5 0·02

0·9 0·95 0·01

Methylcyc/ohexane

DMA

0

62

1·7

0·33

0·25

Acetonitrile

DEA DMA Aniline

40 24 15

49 42 17

1Dimethylformamide

DEA DMA

37 24

44 40

2-8

2·5

Molecular Complexes and Exciplexes

485

Table 9.24 Quenching of anthracene derivatives in carbon tetrachloride

solution64

Fluorescence (CPFM) , - -- --'

Code 3.1 3.1A 3.1C

Compound

Anthracene 9-Methylanthracene 9,1O-DiphenyIanthracene 3.m 9-Phenylanthracene 3.1H 9,1O-Dichloroanthracene 3.1N 1-Chloroanthracene 9-Chloroanthracene

02-free 02-saturated

Solvent reaction (qRM)

Quantum efficiency (max.) of O 2 uptake Sum

0·01 0·01 0'04

0·01 0·01 0·03

0·4 0·22 0·15

0·75 1'3 0'75

1·16 1'53 0·93

0·04 0'53

0·03 0·23

0'156 0·013

0·85 0·89

1'04 1·13

0·05 0·16

0'04 0·09

0'078 0·18

0·45 0'63

0'56 0'90

486

Molecular Complexes and Exciplexes 7

Table 9.25 Rate parameter kQT (in 10 M - 1 S - l) of quenching of triplet naphthalene 80 and triplet anthracene 8 1 by ions in room-temperature solution

Ion K+ Zn H Ga3+ Cu(CN}2" Cu H NiH Co H Cr3+ Fe H Fe3+ Mn H Pr3+ Nd3+ Sm3 + Gd3+

Paramagnetic susceptibility (Bohr magnetons) 0 0 0 0 1-93 3-21 5-01 3-82 5-30 5-85 5-81

Triplet naphthalene ,--~

In H 2 O 0-00 0-0 0-0 0-0 7-5 2-3 5-0 6-9

Triplet anthracene r------A-

In EtGI

In Pyr

0 0 0 7-3 2-4 4-4

InTHF

< 0-004

46 12 6-2

32 16 21 20

3-8 2-9 2-8

1-6

3060

0-04

8-01

0-007

Et 01, ethylene glycol; Pyr, pyridine; THF, tetrahydrofuran_

0-43 < 0-05 < 0-05 < 0-05

0 -13

Molecular Complexes and Exciplexes

487

Table 9.26 Stern-Volmer quenching parameter k of triplet naphthalene·d 8 by ions in rigid solution at 77°K 82

Ion Cu2+ Ni2+ Co 2+ Mn2+ Fe 3 + Gd H

Paramagnetic susceptibility (Bohr magnetons)

k (M- I )

1·93 3·21 5·01 5-81 5·85 8·01

3·4 4·7 4·0 13·2 14·0 20·0

Molecular Complexes and Exciplexes

488

Table 9.27 Temperature dependence of triplet lifetime (TM) of aromatic hydrocarbons in plastic solutions TT

(s)

TT

(77°K)

...... -~

Code

Compound

77°K

298°K

2 2d 3.1 3.1d 3.2 3.2d 4.1 4.1d 4.3 4.3d 4.4 4.4d 4.6 4.6d A Ad D Dd

Naphthalene Naphthalene'd B Anthracene Anthracene·d 1o Phenanthrene Phenanthrene'd 1o pyrene Pyrene'd lO 1 : 2-Benzanthracene 1 : 2-Benzanthracene'd 12 Chrysene Chrysene·d i2 Triphenylene Triphenylene'd l2 Biphenyl Biphenyl'd lO p-Terphenyl p-Terphenyl'd 14

2·4 22 0·048 0·153 3·8 16'4 0·63 3'4 1'04t 1·90 2'0 12·3 16 23 4·2 10·3 2·6 5·3

1·5 12'5 0·025 0·073 2'5 11·7 0·44 2-4 1'02t 1·10 1·2 7·2 9'4 12·2 2'0 5·8 1·3 3·2

t Values questionable,89 cf. Table 5.3. 'TT (77°K) = 0·3 s.

TT

(298°K) 1·6 1·8 1·9 2'1 1·5 1·4 1'4 1·4 (1 '0) 1·7 1·7 1·7 1·7 1·9 2·1 1·8 2·0 1·7

Ref. 86 86 87 87 86 86 88 88 88 88 88 88 86 86 86 86 86 86

9.13 References

489

9.13 References 1. J. B. Aladekomo and J. B. Birks, Proc. Roy. Soc. A, 284, 551 (1965). 2. L. G . Christophorou and R. N . Compton, Health Physics, 13, 1277 (1967). 3. R. S. Mulliken, J. Am. Chem. Soc., 72, 600 (1950); 72, 4493 (1950); 74, 811 (1952); J. Chem. Phys., 19, 514 (1951); 23, 397 (1955); J. Phys. Chem., 56, 801 (1952); J. Chim. Phys., 51,341 (1954); Rec. Trav. Chim. , 75, 845 (1956). 4. S. P. McGlynn, Chem. Rev., 58, 1113 (1958); Radn. Res. Suppl., 2, 300 (1960). 5. G. Briegleb, Elektronen-Donator-Acceptor-Komplexe, Springer-Verlag, Berlin, 1961. 6. H. McConnell, J. S. Ham and J. R. Platt, J. Chern. Phys., 21, 66 (1953). 7. R. M. Hedges and F. A. Matsen, J. Chem. Phys., 28, 950 (1958). 8. R. Foster, Nature, 183, 1253 (1959). 9. J. B. Birks and M. A. Slifkin, Nature, 191, 761 (1961). 10. F. Gutmann and L. E. Lyons, Organic Semiconductors, John Wiley and Sons Inc., New York, 1967. 11. K. Nakomoto, J. Am. Chem. Soc., 74, 1739 (1952). 12. S. K. Lower, R. M. Hochstrasser and C. Reid, Mol. Phys., 4, 161 (1961). 13. G . Briegleb and J. Czekalla, Z. Elektrochem., 59, 184 (1955). 14. H. A. Benesi and J. H. Hildebrand, J. Am. Chem. Soc., 71, 2703 (1949). 15. D. F. Evans, J. Chem. Phys., 23, 1424, 1426 (1955). 16. M. A. Slifkin and A. C. Allison, Nature, 215, 949 (1967). 17. L. E. Orgel and R. S. MuJliken, J. Am. Chem. Soc., 79, 4839 (1957). 18. J. N. MurreJl, J. Am. Chem. Soc., 81, 5037 (1958). 19. N. Christodouleas and S. P. McGlynn, J. Chem. Phys., 40, 166 (1964). 20. S. Iwata, J. Tanaka and S. Nagakura, J. Chem. Phys., 47, 2203 (1967). 21. M. M. Moodie and C. Reid, J. Chem. Phys., 22, 252 (1954). 22. J. Czekalla, A. Schmillen and K. J. Mager, Z . Elektrochem., 61,1053 (1957); 63,623 (1959). 23. J. Czekalla, G . Briegleb, W. Herre and R. Glier, Z. Elektrochem., 61, 537 (1957); J. Czekalla, G . Briegleb and W. Herre, Z. Elektrochem., 63, 712 (1959). 24. J. Czekalla, G. Briegleb, W. Herre and H. J. Vahlensieck, Z. Elektrochem., 63,715 (1959). 25. S. P. McGlynn and J. D. Boggus, J. Am. Chem. Soc., 80, 5096 (1958); S. P. McGlynn, J. D. Boggus and E. Elder, J. Chem. Phys., 80, 5096 (1960). 26. K. B. Eisenthal and M. A. EI-Sayed, J. Chem. Phys., 42, 794 (1965). 27. M. S. Walker, T. W. Bednar and R . Lumry, J. Chem. Phys. , 45, 3455 (1966); 47, 1020 (1967). 28. J. B. Birks, Nature , 214,1187 (1967). 29. J. B. Birks and L. G. Christophorou, Nature, 196, 33 (1962). 30. H. Leonhardt and A. Weller, Z. Elektrochem., 67, 791 (1963). 31. E. A. Chandross and J. Ferguson, J. Chem. Phys., 47, 2557 (1967). 32. N. Mataga, T. Okada and K. Ezumi, Malec. Phys., 10, 203 (1966). 33. A. S. Cherkasov and N. A. Bazilevskaya, Bull. A cad. Sci. USSR, Phys. Ser., 29, 1288 (1965). 34. N. F. Neznaiko, I. E. Obyknovennaya and A. S. Cherkasov, Opt. Spectr. , 21 , 23 (1966); 21, 285 (1966). 35. I. E. Obyknovennaya and A. S. Cherkasov, Opt. Spectr. , 22, 172 (1967). 36. F. Hirayama, J. Chem. Phys., 42, 3163 (1965).

490

Molecular Complexes and Exciplexes 9.13

37. E. A. Chandross and J. Ferguson, J. Chern. Phys., 45, 397 (1966). 38. P. E. Fielding and R. C. Jarnagin, J. Chern. Phys. , 47, 247 (1967). 39. J. Eisinger, M. Gueron, R. G. Shulman and T. Yamane, Proc. Nat. A cad. Sci., 55,1015 (1966). 40. R. M. Hochstrasser, J. Chern. Phys., 36, 1099 (1962). 41. K. Kawaoka and D. R . Kearns, J. Chern. Phys., 45,147 (1966). 42. Y. Ishii and A. Matsui, J. Phys. Soc. Japan, 22, 926 (1967). 43. B. K. Selinger, Nature, 203, 1062 (1964). 44. H. Leonhardt and A. Weller, Z. Phys. Chern. (N.F.), 29, 277 (1961); Luminescence of Organic and Inorganic Materials, p. 74 (Ed. H. Kallmann and and G . M. Spruch), John Wiley & Sons, New York, 1962. 45. H. Beens, H. Knibbe and A. Weller, J. Chem. Phys., 47, 1183 (1967). 46. H. Knibbe, K. Rollig, F. P. Schafer and A. Weller, J. Chem. Phys., 47, 1184 (1967). 47. H. Knibbe, D. Rehm and A. Weller, Z. Phys. Chem. (N.F.), 56, 95 (1967). 48. H. Knibbe and A. Weller, Z. Phys. Chern. (N.F.), 56, 99 (1967). 49. N. Mataga, K. Ezumi and K. Takahashi, Z. Phys. Chern. (N.F.), 44, 250 (1965). 50. N. Mataga, K. Ezumi and T. Okada, Malec. Phys. , 10, 201 (1966). 51. N. Mataga, T. Okada and N. Yamamoto, Bull. Chern. Soc. Japan, 39, 2562 (1966). 52. N. Mataga, T. Okada and H. Oohari, Bull. Chern. Soc. Japan, 39, 2563 (1966). 53. N. Mataga, T. Okada and N. Yamamoto, Chem. Phys. Lett., 1,119 (1967). 54. I. E. Obyknovennaya and A. S. Cherkasov, Doklady Phys. Chem., 173,260 (1967). 55. M. A. F. Tavares, M.Sc. thesis, University of Manchester (1968). 56. J. Klein, Thesis, University of Strasbourg (1968). 57. P. Pringsheim, Fluorescence and Phosphorescence, Interscience, New York, 1949. 58. Th. Forster, Fluorescenz Organischer Verbindungen, Vandenhoeck and Ruprecht, Gottingen, 1951. 59. W. R. Ware and H. P. Richter, J. Chem. Phys., 48, 1595 (1968). 60. M. Kasha, J. Chern. Phys., 20, 71 (1952). 61. T. Medinger and F. Wilkinson, Trans. Faraday Soc., 61, 620 (1965); A. R. Horrocks, A. KearveIl, K. Tickle and F. Wilkinson, Trans. Faraday Soc., 62,3393 (1966); A. R. Horrocks and F. Wilkinson, Proc. Roy. Soc. A, 306, 257 (1968). 62. E. Baur, Z. Phys. Chern., B16, 465 (1932). 63. J. Weiss and H. Fischgold, Z. Phys. Chem. B32, 135 (1936). 64. E. J. Bowen and K. K. Rohatgi, Disc. Faraday Soc., 14, 146 (1953). 65. G. Kallmann-Oster, Acta. Phys. Polan., 26, 435 (1964). 66. E. J. Bowen and J. Sahu, J. Phys. Chem., 63, 4 (1959). 67. O. Stern and M. Volmer, Physik. Z., 20, 183 (1919). 68. S. I. Vavilov, Z. Physik., 53,665 (1929). 69. F. Perrin, C.R. Acad. Sci. Paris, 178, 1978 (1924). 70. J. Bouchard, C.R. Acad. Sci. Paris, 196,485 (1933). 71. A. Jablonski, Acta Phys. Polan., 16, 471 (1957); Bull. Acad. Polan. Sci., Ser. Sci. Math. Astron. Phys., 6, 663 (1958). 72. S. Siegel and H. S. Judeikis, J. Chern. Phys., 48,1613 (1968). 73. J. M. Frank and S. I. Vavilov, Z. Physik., 69, 100 (1931). 74. E. J. Bowen and W. S. Metcalf, Proc. Roy. Soc. A, 206, 937 (1951).

9.13 References

491

75. A. Weller, Progress in Reaction Kinetics, 1, 187 (1961). 76. W. R. Ware and J. S. Novros, J. Phys. Chem ., 70,3246 (1966). 77. W. H. Melhuish and W. S. Metcalf, J. Chem. Soc., p. 976 (1954); p. 480 (1958). 78. M. von Smoluchowski, Z. Phys. Chem., 92, 129 (1917). 79. R. M. Noyes, Progress in Reaction Kinetics, 1, 129 (1961). 80. G. Porter and M. R. Wright, Disc. Faraday Soc., 27, 18 (1959). 81. H. Linschitz and L. Pekkarinen, J. Am. Chem. Soc., 82, 2411 (1960). 82. B. Smaller, E. C. Avery and J. R. Remko, J. Chem. Phys., 42, 2608 (1965). 83. J. W. Hilpem, G. Porter and L. J. Stief, Proc. Roy. Soc. A, 277, 437 (1964). 84. G. Jackson and R. Livingston, J. Chem. Phys., 35, 2182 (1961). 85. J. Langelaar, Thesis, University of Amsterdam (1969). 86. R. E. Kellogg and R. P. Schwenker, J. Chem. Phys., 41, 2860 (1964). 87. A. Beckett, Nature, 211, 410 (1966). 88. R. E. Kellogg and N. C. Wyeth, J. Chem. Phys., 45, 3156 (1966). 89. W. Siebrand, J. Chem. Phys., 47, 2411 (1967). 90. J. W. Longworth, Photochem. Photobiol., 7, 587 (1968). 91. H. Beens and A. Weller, Molecular Luminescence, p. 203 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. 92. H. Hayashi, S. Nagakura and S. Iwata, Molecular Luminescence, p. 351 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. 93. P. F. Jones and S. Siegel, Molecular Luminescence, p. 15 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969; J. Chem. Phys. 50,1134 (1969). 94. H. W. Offen and D. E. Hein, Molecular Luminescence, p. 1 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969. 95. A. Weller and K. Zachariasse, J. Chem. Phys., 46, 4984 (1967); Molecular Luminescence, p. 895 (Ed. E. C. Lim), W. A. Benjamin, Inc., New York, 1969.

10 Interactions with oxygen and nitric oxide 10.1 Oxygen and nitric oxide The oxygen molecule O 2 has a triplet ground state (.E 3;), it is paramagnetic, and it is an electron acceptor (Table 9.1). It has excited singlet states (ILlg, l.Ei) with excitation energies of 7882 cm- I and 13,121 cm- I, respectively. The interaction of ground-state oxygen (30 2 ) with an aromatic molecule (I M) leads to the following photophysical processes: (i) contact CT absorption (§9.4); (ii) enhanced So - TI absorption (§6.8); (iii) triplet eM*) excitation quenching; and (iv) singlet (I M*) excitation quenching. There is evidence, to be discussed in §1O.4, for (v) energy transfer from 3M* to 302 yielding singlet-excited oxygen eoD 3M* + 302

--J>

1M + 101

(10.1)

Singlet-excited oxygen may interact with a ground-state aromatic molecule eM) to give (vi) the peroxidation reaction (§6.2) (10.2) The peroxidation reaction commonly occurs in anthracene and the higher polyacenes. In anthracene peroxide the oxygen molecule bridges the meso (9-, 10-) positions of the anthracene molecule, just as in dianthracene (§7.1O) the bonds between the two anthracene molecules are at the meso positions. In both cases the central ring of the anthracene molecule loses its aromaticity and planarity. When a solution of anthracene containing dissolved

10.2 Contact CT Absorption

493

oxygen is irradiated, photodimerization and photoperoxidation are competing photochemical processes. Nitric oxide (NO) is the simplest stable molecule with an odd number of electrons. It has a doublet ground state XZ IIr • Because of its unpaired electron it is paramagnetic at room temperature (the lowest-lying energy level, XZIIt , is diamagnetic ' ) and it is an electron acceptor (Table 9.1). Ground-state nitric oxide CZNO) may interact with an aromatic molecule eM), in a similar manner to oxygen, to give (i) contact CT absorption; (ii) enhanced So - TI absorption; (iii) triplet CM*) excitation quenching; and (iv) singlet CM*) excitation quenching. However, the lowest excited state (a 4 IIj) of NO is at 37,900 cm- I, I which exceeds the triplet (T I) excitation energies (and almost all the singlet (SI) excitation energies) of the aromatic hydrocarbons. Hence no processes analogous to (v) or (vi), which involve singlet-excited oxygen eOi), can occur with NO. These similarities and differences in the behaviour of Oz and NO are useful diagnostic tools in distinguishing their interactions with aromatic molecules. 10.2 Contact CT absorption

The nature of the physical interaction of oxygen and the origin of the associated photophysical processes have been the subject of several theoretical discussions. z- 6 Figure 10.1 is a schematic diagram of the lower electronic energy levels of the complex M .Oz between an aromatic donor molecule M and an oxygen molecule Oz. The term 'complex' is taken to include 'contact complexes'. The nomenclature of the states of the complex is that introduced by Tsubomura and Mulliken,z that used by Kearns and co-workers5- 6 being shown in parentheses. 1M, 3M* and IM* are the ground singlet, excited triplet and excited singlet states of M. 31:;, ILlg and '1:i are the ground triplet and first two excited singlet states of Oz. The M.Oz states originate as follows: 3A CTo), from 1M, 31:; eT"z), from 1M, 'Llg I(T3)' from 1M, 11:: 1,3.5F (,,3 ,5T 4 ), from 3M*, 31:; 1,3CT (,,3 T eT ), from zM +, 20 2 3G, from IM*, 31:; Tsubomura and Mulliken 2 demonstrated the contact CT nature of the structureless absorption band induced by dissolved oxygen in organic

Interactions with Oxygen and Nitric Oxide 10.2

494

liquids, by observing a correlation between the spectrum and the donor ionization potential I D , similar to (9.39). Contact CT absorption due to dissolved oxygen is not restricted to aromatic liquids. Similar CT absorption bands are observed in saturated hydrocarbons, in cyclohexane, in aliphatic alcohols and ethers,1 and in water containing dissolved oxygen. MurrellS proposed that the intensity of contact CT absorption bands is derived from interaction of the CT state with excited states of the donor 3G ',3CT (1,3 rCT ) 1,3,SF (1,3,5rq ) '0 2' ('I; )

(1r3l

'o~ (b g )

('r1,2)

3A (3 r o) M

302 (3 I ; ) M.02

O2

Figure 10.1 Schematic diagram of the lower electronic energy levels of the M.02 complex between an aromatic donor molecule M and an oxygen molecule O2

or acceptor, as discussed in §9.4. The theoretical studies of Tsubomura and Mulliken2 confirmed this explanation of the phenomenon. In the M.02 complex the contact CT absorption corresponds to the allowed 3A - 3CT transition (Figure 10.1). This derives its intensity from interaction with the 3G state, i.e. from the IM* state of the aromatic donor. When the So - SI transition is optically forbidden, as in benzene, the CT transition is considered to borrow its intensity from a higher excited singlet state of M, via a higher excited triplet state of the M.02 complex. 2 Figure 10.2 is a schematic diagram of the lower electronic energy levels of the complex M.NO between an aromatic donor M and a nitric oxide molecule NO. The 2A, 2,4F and 2G states originate from a combination of 2NO with the 1M, 3M* and IM* states, respectively, and the chargetransfer states 2,4CT from M +, NO- . By analogy to the behaviour of O 2, the contact CT absorption due to NO corresponds to the allowed 2A - 2CT transition, which derives its intensity from interaction of 2CT with 2G, i.e. from the IM* state of the aromatic donor. 10.3 Enhanced So - T I absorption The enhanced So - T J absorption of the aromatic donor 1M in the presence of dissolved oxygen (§6.8) corresponds to the 3A - 3F transition

495

10.3 Enhanced So - T, Absorption

of the contact M.02 complex. Several mechanisms for this enhanced absorption have been suggested. (a) Evans,9 who first observed the phenomenon, associated it with the paramagnetism of the O 2 molecule, and he suggested that a spin-orbit perturbation caused by the inhomogeneous magnetic field of the O 2 molecule might be responsible. A similar enhancement of the So - TI absorption is produced by nitric oxide, 10 but not by paramagnetic cupric, manganous, nickel or cobaltous salts in aqueous, methanolic or ethanolic solutions. 11 In the latter case the solvation sheath of the paramagnetic ion probably 2G - _ -

=== 2,4 F ===

2, 4CT

M

M.NO

NO

Figure 10.2 Schematic diagram of the lower

electronic energy levels of the M.NO complex between an aromatic donor molecule M and a nitric oxide molecule NO prevents its close approach to the aromatic molecule. Evans l ! therefore prepared complexes of 9-anthroylacetone with various paramagnetic ions. He observed marked So - T! absorption bands in the manganous complex, and weaker bands in the cobaltous, nickel and ferric complexes, but no bands were observed in the gadolinium and dysprosium complexes. The magnetic moments of the gadolinium and dysprosium ions exceed that of the manganous ion, and the ionic radii are similar. Evans concluded that the enhanced So - TI absorption was not due to an inhomogeneous magnetic field effect. Calculations by Tsubomura and Mulliken 2 have shown that the magnetic perturbation is negligible, and that the absorption enhancement is associated with charge-transfer. (b) Since the 3A and 3F states of the M.02 complex are of the same multiplicity, there might be a significant transition probability between them, even in the absence of perturbations by other states. Tsubomura and Mulliken 2 considered the most favourable arrangement of the M.02 complex, and they concluded that the unperturbed 3A - 3F transition moment is too small to account for the observed So - TI absorption.

496

Interactions with Oxygen and Nitric Oxide 10.4

(c) Hoijtink 3 proposed that the 3A - 3F transition gains its intensity by direct interaction between the 3F and 3G states, which effectively introduces a component of singlet character M*) into the molecular triplet state eM*). On this model the intensity of the induced So - TI absorption should increase with that of the So - SI absorption. Contrary to this prediction, the So - SI absorption intensity of fluorobenzene is six times that of benzene, but the induced So - TI absorption intensities of the two compounds for a given oxygen concentration are practically the same 4 • 9 (Figure 6.3). Other authors 2. 4 who have considered this mechanism have concluded that it is less important than the following. (d) Murre1l 4 and Tsubomura and Mulliken 2 proposed that the 3A - 3F transition gains its intensity by interaction between the 3F and 3CT states. The intensity of the 3A - 3CT transition, which corresponds to the contact CT absorption, is derived from the 3G state, so that the proposed mechanism provides indirect mixing of the 3G and 3F states, via the intermediate 3CT state, in contrast to the direct mixing considered by Hoijtink. 3 The matrix element for indirect mixing via the 3CT state is calculated to be much larger than that for direct mixing, and to be of the proper order of magnitude to account for the enhanced So - TI absorption intensity.2 Due to the mixing with the 3CT state the Orinduced So - TI absorption is expected to be more diffuse and slightly red-shifted relative to the unperturbed molecular So - TI absorption, and the predicted red shift of ~40 cm- I has been observed in pyrazine. 6 The enhanced So - TI absorption due to nitric oxide 1o can be explained in a similar manner. The allowed 2A - 2F transition gains its intensity from the indirect mixing of the 2G and 2F states, via the intermediate 2CT state (Figure 10.2). The contact CT absorption and enhanced So - TI absorption due to O 2 and NO thus originate from two common properties. (i) The acceptor molecule is paramagnetic, with a ground-state multiplicity m > 1, so that there are lilA, "'F, mCT and mG states of the complex with an aromatic donor. (ii) The electron affinity AA of the acceptor is insufficient to form a bound DA complex, but it is sufficient to form a mCT state of the complex which is intermediate in energy between the mF and mG states, and which provides indirect mixing of these states.

e

10.4 Quenching by oxygen Figure 10.3, which is an extension of Figure 10.1, shows the zero-order states of the M.02 complex of energy ~ SI M*) for naphthalene and anthracene. The energies of the 3M*, 3M** and IM* states are taken from Tables 5.4 and 6.10. The charge transfer (CT) states, 1.3(M+.Oi), are

e

10.4 Quenching by Oxygen

497

assumed to be midway between 3M* and IM* , which places them above the lower energy limit obtained from the O 2 contact CT absorption edge (9.39). The M.02 states are arranged in manifolds according to their multiplicity. The M.02 triplet ground state will be referred to as 3E o, and its singlet, triplet and quintet excited states as lEt ... IE~, 3Et ... 3E~, and 35.--------------------------------------,

30

25

'M·- ',-3,-5,-

15

'210

b,5

o

'M-

N

3 N.0 2

5

A

3

5

A.02

Figure 10.3 Zero-order states of the M.Ol complexes of naphthalene (N) and anthracene (A), arranged in multiplet manifolds

5Et, 5Ei, respectively. The order of the states is the same in naphthalene and anthracene, which will be considered as typical. Calculations by Khan and Kearns 6 indicate that the IEj and 3Et [= I,3e M* .02)] states have a binding energy of ~300 cm- i , due to stabilization by interaction with the 1,3CT states. The 3E o, lEt, lEi and 5Et states are dissociated. The IE:,5 and 3Ei.3,4,5 states are probably bound.

498

Interactions with Oxygen and Nitric Oxide 10.4

Figure 10.4 shows the radiationless transitions that may occur (in naphthalene or anthracene), following the interaction of 302 with 1 M* to form the exciplex 3Er. Spin-allowed transitions are indicated by full lines, and spin-forbidden transitions by broken lines. The experimental and

~.

+

1M

+

I L _'M

+

I I

I I

I I

Figure 10.4 Radiationless transitions following interaction of J0 2 and I M*. Solid lines, spin-allowed transitions; broken lines, spin-forbidden transitions

theoretical data may be combined l2 to determine the most probable transitions. Spin-forbidden transitions in competition with spin-allowed transitions that involve similar energy gaps, i.e. similar Franck-Condon factors , can be neglected. In fluid solutions, where dissociation can occur, this criterion excludes all spin-forbidden transitions, including those between quasi-degenerate states (e.g. lEj, 3Et, 5En. Evidence that the latter are improbable, even in rigid solutions, will be considered in §1O.7. The letters a, b, etc. denote the various radiationless transitions and their rates. Primes denote dissociation processes.

10.4 Quenching by Oxygen

499

In fluid solutions 30 2 collisional quenching of I M* is a diffusioncontrolled process of high reaction probability p (§1O.8) so that

b>a'

(10.3)

indicating that 3E~ is bound. The internal conversion processes within the 3E* manifold, (b, c, e, h) have an estimated rate of _10 12 S-I, so that if the 3Ei,2,3,4 states are bound, 6 it is to be expected that

c,e,h > d',!',g'

(10.4)

i.e. 3E~ internal conversion to 3Ei occurs without dissociation into IM** + 30 2 (d'), 3M* + loi (j'), or 2M+ + 20 2 (g'). There is no experimental evidence for (g'), and evidence that (f') does not occur will be considered later. On the other hand, the products of (d') followed by (k) are indistinguishable from those of (i'). The sequence (d' k) would be eliminated in a compound in which there is no 3M** state below IM*, e.g. pyrene (§6.13). Processes (i') and (j) are the spin-allowed radiationless transitions competing for the 3E* excitation energy. In fluid solutions at room temperature, where the 3Ei binding energy -kT, it is to be expected that i' >j

(10.5)

since process (j) involves a small Franck-Condon factor. In viscous or rigid solutions, where the dissociation (i') is inhibited, it is to be expected that the inequality will be reversed and

j> i'

(l0.5a)

The sequence (abcehi') corresponds to the overall process IM*

+ 30 2 --+ 3M* + 30 2

(10.6)

The sequence (abcehjo') corresponds to the overall process IM*

+ 30 2 --+ 1M + 30 2

(10.7)

The less probable sequence (abcf') would lead to IM*

+ 30 2 --+ 3M* + loi

(10.8)

The sequence (abcehqlm'n), or other sequences involving spin-forbidden processes, would lead to (10.9) Kinetic studies to distinguish between the alternatives (10.6)-(10.9), which are discussed in §1O.5, support the conclusions of the model, i.e. that (10.6) occurs in low-viscosity solutions, and that (10.7) occurs in viscous and rigid solutions. 17

500

Interactions with Oxygen and Nitric Oxide 10.4

Figure 10.5 shows the radiationless transitions that may occur (in naphthalene or anthracene) following the interaction of 30 2 with 3M* to form an exciplex I Ej, 3Et or 5Et. Under the same diffusion conditions as for the 1M * quenching (Figure 10.4),

a=t + i + s

(10.10)

so that assuming multiplicity weighting between the alternative exciplex states (10.11) t = a/9; i = a/3; s = 5a/9

3M "

II

+

--- ~ E~

5'

3 02

::-// 1

_,_ . ~

;'

/ /, I t II

3E; /, 1< r p' l p , ...... ,q

Q~ ' ~

I

'E 3

t'

---""--

M0 2

jL 'M

+

'M

+

102-

m

n~

+

)~ E

1

I x

'M

v

10~

'E 2

I I I I

+

30 2

~3Eo

Figure 10.5 Radiationless transitions following interaction of 30 z and 3M*. Solid lines, spin-

allowed transitions; broken lines; spin-forbidden transitions

For anthracene in hexane solution at 20°C, kOT = 4 X 10 9 M - I S- I for 30 2 quenching of 3M*,13 compared with kOM = a = 3·5 x 10 10 M - 1 S- I for 30 2 quenching of I M*. Since the diffusion conditions are identical, the probability of quenching at each 3M* - 30 2 encounter is p ~ kOT/ koM ~ 1/9. This indicates that the 3M* quenching occurs predominantly via IEj, and that 3Et and 5Et each dissociate into the original species, i.e.

1+ w> t',p,q' i'>j,q,r s' ~ p',r'

(10.12) (10.5b) (10.13)

10.4 Quenching by Oxygen

501

(l O.Sb) is consistent with the previous conclusions, and (10.13) is consistent with ·the dissociative nature of 5Ei. In viscous or rigid solutions (10.Sb) will be replaced by (lO.Sa). Kawaoka, Khan and Kearns 5 have made a theoretical study of the quenching of 3M* by 30 2 • They considered the two possible quenching processes: (j 0'): enhanced 3M* -

IM

intersystem crossing

3M* + 30 2 ---+ 1M + 302

(10.14)

(t 1m' n), (t luv'): energy transfer from 3M* to 10i,

3M*

+ 302 ---+ 1M + lOr

(l0.1)

a process originally proposed by Kautsky.14 In the M.02 complex (Figure 10.1), (j) corresponds to the 3r 4- 3ro radiationless transition, and (l) and (lu) to the I r 4 - I r3 and I r 4 - I rI.2 radiationless transitions. Kawaoka et al. 5 considered the direct mixing of the initial and final states, and indirect mixing of these states via coupling to either the 3rCT or I rCT states. The matrix elements for indirect mixing are a factor of ~ 10 larger than those for direct mixing, showing that indirect mixing via the CT states plays a similar role to that in induced So - T J ro - 3r 4 ) absorption [§1O.3(d)]. The rate of a radiationless transition

e

(S.17) is the product of a state-density factor P, an electronic factor C lu and a Franck-Condon factor F. The ca1culations 5 indicate that C lu is of similar magnitude for (j), (lu) and (l), and it is concluded that the relative rates of the three transitions are determined by the respective values of F. F was estimated for the three competing processes from the respective energy gaps, ET, ET - IL1 g' and ET - 11:;, assuming the Siebrand relation (Figure S.2) determined for radiationless transitions in unsubstituted aromatic hydrocarbons (§S.9). For a triplet state energy ET = 19,000 cm- I , F is thus estimated as 1· S x 10- 4, 1·S X 10-2 and 0·1 for the 3r 4- 3ro (j), I r 4- J r1.2 (lu) , and I r 4- I r3 (l) radiation less transitions, respectively. Kawaoka et al. 5 conclude that 302 quenching of 3M* yielding lOr (10.1) is more important by a factor of ~103 than process (10.14). In terms of Figure 1O.S, l '?> j (lO.1S) The photoperoxidation reaction (w), which is an alternative potential product of I Ej, would further increase the rate of I Ej quenching, but there is evidence (§1O.S) that (l0.16)

502

Interactions with Oxygen and Nitric Oxide 10.5

Since IEj and 3Et have similar binding energies 6 t /t'~i /i'

(10.17)

and , from (10.11), i = 3t, we obtain in low viscosity solutions (e.g. hexane at room temperature) l ~ i '> t' > j (10.18) which is consistent with (10.l2), (10.5) and (1O.l5). In high viscosity or rigid solutions (I0.5a) replaces (10.5), and (10.18) becomes l ~ j > i' > t'

(l0.18a)

The above discussion indicates that of the alternative IM* quenching processes (10.6)- (10.9), (i') IM*

+ 30 2 -J>- 3M* + 30 2

(10.6)

should be the dominant process in low-viscosity solutions, and (j) IM*

+ 30 2 -J>- 1M + 30 2

(10.7)

should be dominant in viscous or rigid solutions, and that of the alternative 3M* quenching processes (10.14) and (10.1) (10.l) is always dominant. The alternative IM* quenching process (f') IM*

+ 30 2 -J>- 3M* + loi

(10.8)

is only energetically possible if the IM* - 3M* energy gap LiST exceeds the loi Lig) energy. This condition is satisfied by naphthalene and fluorene, but not by phenanthrene and chrysene (Table 5.4). The experimental kQM values of the 30 2 quenching of these four compounds in cyclohexane solution are similar,15 showing that the potential presence or absence of (10.8) does not affect kQM (see p. 634).

e

10.5 Photoperoxidation studies

Experimental confirmation of the modes of quenching of IM* and 3M* by 30 2 is obtained from the study by Stevens and Algar l6 of the photoperoxidation quantum yield lP M02 and fluorescence lifetime T of tetracene in benzene at 25°C as a function of [30 2 ], The following reaction scheme was used for analysis : IM* IM*

-J>-J>-

1M + hVM 3M*

1

2

10.5 Photoperoxidation Studies

503

IM*---!> 1M IM* + 302 ---!> 3M* + 302 IM* + 302 ---!> 3M* + loi 3M*---!> 1M 3M* + 302 ---!> 1M + loi 3M* + 302 ---!> 1M + 30 2 1M + loi ---!> M0 2 loi ---!> 302

(kGM) (10.6) (10.8) (kT) (10.1) (10.14) (10.2)

3 4 5 6 7 8 9 10

For completeness the following two processes may be added : IM*+30 2 ---!>IM+30 2 IM* + 30 2 ---!> 1M + loi

(10.7) (10.9)

11 12

k j is the rate parameter of the jth process. Schenck 17 has proposed an alternative mode of peroxidation, 3M* + 30 2 ---!> 3M* ... 302 ---!> MO z

13

via a metastable complex 3M* ... 30 z, which he describes as a 'moloxide'. The 'moloxide' is equivalent to the exciplex state 1,3,5 T 4 , and the proposed mode of peroxidation corresponds to process w (Figure 10.5). Khan and Kearns 6 conclude that, although 1,3 T4 has a moderate binding energy of ~300 em-I, the exciplex is too short-lived «10- 10 s) against radiationless transitions (j, I) to the lower lying dissociative T 3 ,2, 1,0 states (Figure 10.1) to be identified as the oxygen-transferring intermediate, so that I~

w

(10.16)

It is observed that ctJ M02 increases with [I M], but is independent of light intensity,16 indicating that the peroxidation occurs by process 9, rather than by process 13. There is further spectroscopic, 18 - 19 analytical,20-22 and kinetic 23 - 24 evidence that the photoperoxidation involves the loi (lLl g ) state as an intermediate (see p. 634). Stevens and Algar l6 analysed their data in terms of ctJ M02 TM/T, where TM is the IM* fluorescence lifetime when [30 2 ] = O. For k6 ~ (k7 + ks) [30 2 ],

ctJ MO TM/T = 4> {C k 5 + k I2 ) [30 2 ] + ~ (k2 + -'Ck -.,---:4_+_k-,-:5-'.) ,,[3--,-0=2])} 2 kl+k2 + k3 k7 + k s kl + kz + k3 (10.19) where (10.20) 4> = k 9 [lM] /(k 9 [lM] + klo) TM _

T

1 = (k 4 + k5 + kll + k 12 ) [30 z]

kl + k2+k3

(10.21 )

504

Interactions with Oxygen and Nitric Oxide 10.6

Assuming either processes 4 or 5, either 7 or 8, and either 11 or 12 to be operative, the possible modes of 101 production yield the following relations. (i) From I M * only (k 4 = k7 =

kll

= 0) (10.22)

If>Mo z TM IT = c/>(TMIT - 1)

(ii) From 3M* only (k s = kg = kl2 = 0) If>Mo z TMIT

= c/> {If>TM + k4 ~4k II (TMIT -

I)}

(10.23)

where If>TM

=

k2/(kl

is the 3M* quantum yield for [30 2 ]

=

+ k2 + k3)

(10.24)

o.

(iii) From IM* and 3M* (k 4 = kg = kll = 0) (10.25)

Stevens and Algar l6 showed their data to be inconsistent with (10.22), and also with (10.25) if kl2 = O. They analysed their results in terms of (10.23) with kll = 0, i.e. (10.26) The values of If>TM obtained from (10.26) agree satisfactorily with theory (§6.3). If k s = 0, equation (10.25) also reduces to (10.26). There are thus two alternative schemes which are consistent with the photoperoxidation data: (a) ks = kg = kll = kl2 = 0, as proposed by Stevens and Algar,16 and (b) k4 = ks = kg = kll = 0. Both schemes show that 3M* quenching occurs by process (10.1) yielding 101, and that the IM* quenching does not occur by processes (10.7) or (10.8). They differ in the I M* quenching mechanism IM* + 30 2 -+ 3M* + 302 (4) (10.6) IM*

+ 30 2 -+ 1M + 101

(12)

(10.9)

Process (10.6) is preferred, since it is consistent with the exciplex model (Figure 10.4) and with the other experimental and theoretical data discussed in §1O.4. 10.6 Quenching by nitric oxide

Figure 10.6 shows the radiationless transitions that may occur following the interaction of 2NO with 1M* or 3M*.12 The letters A, E, etc. denote

10.6 Quenching by Nitric Oxide

505

the various radiationless transitions and their rates, and primes denote dissociation processes. Spin-allowed and spin-forbidden processes are indicated by full and broken lines, respectively.

1-

1M li C' (10.28) and 2Ej is internally converted to 2Ei:- By analogy to the behaviour of 302 (§1O.4) it is to be expected that E'>G (10.29) in low-viscosity solutions, and that G > E' in viscous or rigid solutions.

(l0.29a)

506

Interactions with Oxygen and Nitric Oxide 10.7

3M* and 2NO interact (E, F) to form an exciplex 2.4Er in a doublet or quartet state. Under common diffusion conditions, assuming multiplicity weighting (10.30) E=A/3; F= 2A/3

Porter and Windsor l3 reported similar values of k QT (02) = kQT(NO = 4 x 109 M- I S- I for the 30 2 and 2NO quenching of triplet anthracene in hexane solution at 20°C. Subsequent measurements indicate that this value of kQT(NO) is too high. Kusuhara and Hardwick 27 observed the 2NO quenching of triplet anthracene and triplet tetracene in hexane solution from 20°C to - 30°C, and they obtained 20°C values of kQT(NO) = 1·5 x 108 M - I S- I and 2·1 x 108 M- I S- I , respectively. Siegel and Judeikis 28 observed k QT (02) = 230 M- I S- I and kQT(NO) = 24 M - I S- I for the quenching of triplet naphthalene in 3-methylpentane fluid solution at 87°K. These authors also observed the effect of dissolved O 2 and NO on the triplet lifetime of naphthalene'd 8 in 3-methylpentane glass solutions at 77°K. (10.31) where (kT)Q is the reciprocal of the triplet lifetime in the presence of [Q], and kQT is the dynamic triplet-quenching rate parameter. The data 28 are consistent with (10.31), and they yield values of k QT(02) = 0·23 M- I S-I and kQT(NO) = 0·018 M- I S-I . It thus appears that k QT (02) ~ 10-20 kQT(NO) for solutions from 77°K to 293°K. This difference in the tripletquenching behaviour of O 2 and NO provides further indirect evidence for process (10.1) which yields lOr. It is concluded that I> G

(10.32)

or, expressed in terms more appropriate to quenching in viscous or glassy solutions, (10.33) where RQT is the range of the appropriate quenching interaction. 10.7 Static quenching

Siegel and ludeikis 28 have studied static quenching by observing the effect of dissolved O 2 , NO and Xe on the photostationary triplet concentration [3M*]s of naphthalene·d 8 in 3-methylpentane glass solutions at 77°K. The system was excited into 1M * by steady illumination of very weak intensity 10, and the relative values of [3M*]s were determined from the 3M* electron spin resonance signal and the phosphorescence intensity as functions of [Q]. They observed a decrease in the triplet quantum yield (6.6)

10.7 Static Quenching

507

and they attributed this to static quenching of the naphthalene triplet state. The data were analysed using a relation analogous to (9.82). ( 2 X 10-5 , (TM)y decreases, due to the onset of the radiationless transfer process which competes with the host fluorescence. The simultaneous occurrence of radiative and radiationless transfer led to much confusion of interpretation in the earlier literature, and attempts to explain energy transfer in terms of one or other of these processes. It is now clear that both processes can occur simultaneously, their relative importance depending on several factors, including the specimen thickness and acceptor concentration. Even when radiative migration or transfer is not the dominant process, its presence may influence or distort observations of the radiationless processes. Kucherov and Faidysh46 and Faidysh and Zima62 have studied the influence of the specimen thickness d on energy transfer in anthracene-

11.5 Triplet-Triplet Energy Transfer in Solution

537

tetracene mixed crystals. Typical results showing the thickness dependence of the ratio /FY j /FM of the relative intensities of the tetracene and anthracene fluorescence components at two different concentrations Cy are plotted in Figure 1l.3. /FY j /FM increases with Cy, but for comparison purposes the values for the two concentrations are normalized at d = 0·2 ,urn. Two effects may be distinguished. The sharp decrease in /Fy j /FM with d from 1 ,urn to 0·2 ,urn is attributed to competition betwee.n surface defects and tetracene molecules for the excitons. The decrease is greater in the system with the smaller tetracene concentration. The increase in /Fy j / FM at greater thicknesses is due to radiative migration. Self-absorption of the anthracene fluorescence within the crystal regenerates excitons, thereby increasing their effective lifetime and migration length and their probability of capture by a tetracene molecule. The effect is more marked at the lower concentration because of the greater anthracene fluorescence intensity. The effect of finite self-absorption aMM (11.23) is to increase the technical quantum efficiency of radiationless transfer to ly fromjYM, given by (1l.30), to (f, ) = k yM [1y] (1l.41) YM a kFM(1- aMM ) + kiM + kyM[ly] Equation (1l.41) has been shown63 to be in good agreement with the observations of Kucherov and Faidysh. 46 In addition to radiative migration,

radiative transfer is also important in thick specimens, particularly at low Cy . The results show the complexity of the energy migration and transfer processes in mixed crystals in which the host exhibits strong self-absorption. In this respect anthracene, which has been selected by many observers as a representative aromatic crystal, is a somewhat unfortunate choice. Due to the strong self-absorption, the fluorescence (exciton) lifetime decreases from -30 ns for a crystal of a few mm thickness to 10 ns for one of a few ,urn thickness, and in small crystals it may decrease to -3 ns due to surface defects or oxidation. 29 The study of an aromatic host crystal which is transparent to its own fluorescence (e.g. p-terphenyl) would eliminate the influence of radiative migration on other photophysical processes. 11.5 Triplet-triplet energy transfer in solution Triplet-triplet energy transfer was first clearly demonstrated by Terenin and Ermolaev,64 who excited the phosphorescence of an acceptor (naphthalene) by triplet transfer from a donor (benzophenone) in rigid solution at 77°K. The energy Eex of the exciting light and the singlet excitation energies, ESM and E sy , of the donor (M) and acceptor (Y) molecules were chosen such that (1l.42)

538

Energy Migration and Transfer 11.5

so that only the donor molecules were excited initially. The triplet excitation energies, ETM and E Ty , of M and Y were such that (11.43)

ETM - ETY = Ll TMy > 0

thus providing the energy condition for triplet-triplet transfer following IM* - 3M* intersystem crossing. The observed increase in the 3y* phosphorescence intensity with acceptor concentration pY] and the simultaneous quenching of the 3M* phosphorescence intensity gave clear evidence for the process, (11.11) The static quenching of the donor phosphorescence yield qJPT by triplettriplet energy transfer is described by the active sphere model (9.82), qJPT (qJPT)o

=

e-k' [ly]

(11.44)

where R YT , the radius of the active sphere, is given by (9.84), _ ( 3k' RYT - 47TN'

)1/3

(11.45)

Ermolaev6 5 studied other rigid solution systems, satisfying conditions (11.42) and (11.43), and his results are listed in Table 11.5. The values of ETY are similar for naphthalene and its halogenated derivatives, although halogen substitution causes a large increase in the acceptor So - TI transition dipole moment by the internal heavy-atom effect (§6.7). The observation that RYT is independent of this parameter (Table 11 .5) shows that the triplet-triplet transfer is not due to dipole-dipole interaction. The magnitude of RYT is consistent with electron-exchange interaction. Backstrom and Sandros67 studied triplet-triplet transfer in benzene solutions at room temperature. Biacetyl (ETM = 19,700 cm- I) was used as the donor, since it is one of the few substances which phosphoresces efficiently in room temperature fluid solutions. They observed the rate parameter kQT for the quenching of the phosphorescence of biacetyl due to triplet-triplet energy transfer to various acceptors, and they also evaluated the energy transfer rate parameter k yT , corrected for back transfer. By analogy to (9.73) and (9.74), under photostationary conditions kyTky

kQT = (k y

+ kTYP MD

where k y is the rate of 3y* decay (for PM] meter of the back transfer process

=

(11.46)

0), and kTY is the rate para(11.1la)

11.5 Triplet-Triplet Energy Transfer in Solution

539

68

Figure 11.4 pl ots log] OkQT (open circles) and log] okYT (full circles) against the acceptor triplet excitation energy ETY , from the data of Backstrom and Sandros. 6 7 The magnitude of the electron-exchange interaction depends on the overlap of the vibronic wavefunctions of the donor and acceptor molecules.

10

9

-

.... 7 -

\

o

"'" .3'"

\

-\

6

0\

\ \ \

5 ET biocetyl

4

14,000

16 ,000

Figure 11.4 Triplet-triplet energy transfer from

biacetyl to various acceptors in benzene solutions at room temperature. Rate parameter against triplet energy ET of acceptor. 0 k QT , observed quenching rate parameter; • k yT , energy transfer rate parameter corrected for back transfer (11.46) (after Backstrom and Sandros,67 and Lamola68) The transfer probabil ity by electron-exchange interaction can be expressed in the form (Dexter 69 )

f PT(ii) Ey(ii) dii 00

kYT oc (27T/h) Z2

(11.47)

o

where PT(ii) is the donor emission spectrum, Ey(ii) is the acceptor absorption spectrum, and Z2 is a parameter which cannot be directly related to optical parameters. Although electron-exchange interaction depends on spectral (i .e. wavefunction) overlap, it differs from Coulombic interaction and radiative transfer in that it is independent of the optical transition moments.

Energy Migration and Transfer 11.5

540

The data of Figure 11.4 show three regions of interest. (i)

..d T MY > 1500 cm- I • Here kQT = kYT = kdif( , the rate parameter of a diffusion-controlled process, showing that the triplet-triplet energy transfer in low-viscosity fluid sofutions occurs collisionally E TM -

ETY =

(11.7)

and that 3M * quenching occurs with p = 1. (ii) 1500 cm- I > ..d TMy ;;;' O. Here k YT decreases due to the reduced spectral overlap (11.47), down to a value of (kyT)o at ..d TMy = 0, where only the o - 0 bands overlap. (iii) ..d TMy < O. Energy transfer still occurs but at a much slower rate. This endothermic transfer requires thermal activation, which produces spectral overlap of the 'hot bands' (§3.2). In this region it is to be expected that k YT

=

(kyT)o exp

(-..d TM y/kT)

(11.48)

a relation which agrees closely with the experimental data. Porter and Wilkinson 70 studied the quenching of the triplet donor eM*) and the sensitization of the triplet acceptor ey*) in fluid solutions at room temperature, using flash photolysis to study the donor decay time. They observed little or no dependence of the transfer efficiency on t~e dipole transition moment of either the donor or the acceptor. Their data on the dependence of the rate parameter kQT of quenching due to triplet-triplet transfer on the donor-acceptor energy gap ..d T My are listed in Table 11.6. Smaller et a/.7l studied triplet-triplet transfer from phenanthrene·d lo to naphthalene'd g in viscous solutions at 87°K. They observed by E.S.R. the decay of the donor triplet concentration [3M*] and the rise and decay of the acceptor triplet concentration pY*], following flash excitation. They also observed the photostationary concentrations PM *]s and pY*]s of the two species. The solvents, which were mixtures of methylcyclohexane and cyclopentane, covered a viscosity range fiom Y) = 1·38 X 104 P to 7.35 x 106 P. The results are listed in Table 11. 7. Because of the long triplet lifetime 'TT, the mean diffusion distance V6D'TT ~ R YT , the range of the triplettriplet exchange interaction, and the observed constancy of kyTy) shows that the energy transfer is diffusion-controlled. The experimental values of I kyTy) exceed that of kdiffy) (= 8RT/3000) = 1·95 x 10 7 M- S-I P, evaluated from the Stokes-Einstein relation, indicating that the interaction radius R YT exceeds the collisional radius. A value of R YT = 16 A is obtained from the static triplet-triplet transfer (11.45) between phenanthrene'd lO and naphthalene·d g in EPA solution at n OK . A rather higher, and less reliable, value of R YT = 22 A is obtained by neglecting the diffusion in the most viscous solution at 87°K.

11.5 Triplet-Triplet Energy Transfer in Solution

541

72

Nordin and Strong have discussed the influence of back transfer (rate parameter k TY ) on triplet-triplet energy transfer under transient (flash photolysis) conditions. The reaction kinetics are analogous to those of a monomer-excimer system (§7.3). The molar concentrations of the donor and acceptor exhibit the following time (t) dependence:

[3M*]

oc

e-A1 t

[3y*] oc

+ A e-A2t

e-A1 t _

e-A2 t

(11.49) (11.50)

where AI ,2 = ·H F + G i= {(G - F)2 F

=

kT

G = ky

+ 4k YT k TY PM] Py]}I /2]

+ kYTPY] + kTY[IM]

(11.51) (11.52) (11.53)

and kT and k y are the unquenched 3M* and 3y * decay rates, respectively. Since Al < A2 , at large t [1M*] and [3y*] decrease exponentially with a common decay parameter Ab and it is this parameter which is observed in flash photolysis studies 70 - 71 of triplet-triplet transfer, The observers have assumed either that Al = kT + kQT PY] (Table 11.6) or that Al = kT + kYT [Iy] (Table 11.7). These assumptions are only valid if the back transfer rate kTY [1M] is negligible, under which conditions Al = F and kQT = k YT • In general, however, Al is given by (11.51). Nordin and Strong 72 have pointed out that if kT > k y , it is possible to obtain a value of Al < kT corresponding to 'negative quenching' of 3M*. After an initial fast decay (A2) which would usually occur during the lifetime of the flash, the 3M* population is enhanced by the reverse energy transfer process from 3y*. These complexities do not arise in photostationary measurements of triplettriplet energy transfer, which are described by (11.46). The photostationary studies of triplet-triplet energy transfer (Figure 11.4) thus provide more reliable data on kQT and kYT than the flash photolytic studies [Tables 11.6 and 11.7 (a)] unless the latter are reanalysed in terms of equation (11.51) (see p. 635). Triplet-triplet interaction between molecules of the same species leading to P-type molecular and excimer delayed fluorescence 3M* + 3M* -+ 1M + 1M* 3M*

+ 3M* -+ 1D*

(11.15) (11.16)

has been discussed in Chapter 8. In a fluid solution containing donor (M) and acceptor (Y) molecules, excited by light of low intensity such that [1M*] ~ [lY], the diffusion-controlled rate of 3M* - 3M* interaction by (11.15) and (11.16) is less than that of triplet-triplet energy transfer (11.11)

542

Energy Migration and Transfer 11.5

Under these circumstances the donor delayed fluorescence is quenched, and the system may exhibit sensitized P-type delayedjluorescence of the acceptor. The latter is produced by (11.11) followed by one of the following processes: 3y*+3y*---,?-ly + ly* 3y* + 3y* 3M* + 3y*

---'?-

(1l.l5a)

ID~

(IU6a)

1M + ly*

(lU8b)

---'?-

where 1D~ is the singlet excimer of Y. Processes (I l.15a) and/or (I l.l6a) occur with acceptor molecules which exhibit normal P-type molecular and/or excimer delayed fluorescence when excited directly. The heteropolar triplet-triplet interaction process (1l.18b) can also occur with acceptor molecules which do not yield direct P-type delayed fluorescence. Parker?3 has obtained evidence for this from observations of mixed ethanolic solutions of anthracene (M) and tetracene (Y). According to Parker, a solution of tetracene does not exhibit P-type molecular delayed fluorescence (11.15a). t This is attributed to the fact that the tetracene triplet excitation energy ETY = 10,300 cm- i is less than half its singlet excitation energy Esy = 21,200 cm- i (Table 5.4), so that proct;ss (I l.15a) is endothermic and requires thermal activation. On the other hand, the anthracene triplet excitation energy ETM = 14,700 cm- i , so that ETM + ETY - Esy = 3800 cm- l , and (I 1.18b) is an allowed exothermic process which yields sensitized molecular delayed fluorescence of tetracene in the mixed solutions. Process (I l.l8b) may occur by electron-exchange interaction or via singlet exciplex formation 3M* + 3y* ---'?- I(M.Y)* (11.19) and dissociation. There are several further processes which may occur in mixed solutions of this type. Provided that Esy - 2ETY < By (11.54) where By is the excimer binding energy of I D~, process (I1.l6a) is exothermic, and it can yield sensitized delayed excimer fluorescence. In the case of tetracene, where the excimer interaction is strong, it can alternatively lead to sensitized photodimerization. If the I(M·Y)* exciplex is bound, process (11.19) can yield (i) delayed ly* fluorescence (lU8b), (ii) delayed I M* fluorescence, from the alternative mode of dissociation of I(M·Y)*, (IU8c) t Other observers have recorded P-type delayed fluorescence from tetracene solutions. 20o

11.5 Triplet-Triplet Energy Transfer in Solution

543

(iii) delayed I(M'Y)* exciplex fluorescence, or (iv) stable 'mixed photodimers' of M and Y. There are also the competing processes,

+ 3y* ---7 1M + 3y** 3M* + 3y* ---7 3M** + Iy

3M*

(ll .20) (11.20a)

which can occur by electron-exchange interaction, by triplet exciplex 3(M'Y)* formation and dissociation, or by long-range radiative or dipoledipole transfer. These correspond to the quenching of 3M* and 3y*, respectively. Phosphorescence of each of the three triplet species 3M*, 3y* and \M'Y)* is possible, but their quantum yields are usually negligible in room-temperature fluid solutions. Parker and Joyce 74 have used observations of sensitized P-type delayed fluorescence to determine relative values of the donor triplet quantum yield (/>TM (§S.9). The anthracene (M)-perylene (Y) solution chosen by these authors satisfies the condition Ll TMy > 0 (11.43) for triplet-triplet transfer (11.11), but unfortunately it does not satisfy the condition (11.42) since ESM - Esy = 3700 cm- I (Table 5.4). The prompt Iy* fluorescence excited directly by the incident radiation (perylene has a high extinction coefficient in the region of the anthracene absorption), or by immediate energy transfer from 1M * (11.13) IM* + Iy ---7 1M + Iy* which occurs efficiently in the anthracene-perylene system, can be readily distinguished from the delayed Iy* fluoresence by spectrophosphorimetry. In the analysis (§S.9) it is assumed that the delayed Iy* fluorescence is produced only by 3M* - 3y* transfer (11.1 1) followed by 3y* _ 3y* interaction (11 .15a). However, there are several alternative processes which can also yield delayed Iy* fluorescence. (a) Any Iy* excited directly by the incident radiation, or by energy transfer from IM* (11.13), will yield some 3y* by intersystem crossing ((/>TY is small for perylene). (b) 3M* - 3M* interaction (11.15) leading to IM*, followed by IM* - Iy * energy transfer (11.13), which leads to delayed Iy* fluorescence. (c) The heteropolar 3M* - 3y* interaction process (l1.1Sb) represents a further source of delayed Iy*. The presence of components (a), (b) and (c), together with the experimental difficulty of comparing prompt and delayed fluorescence intensities (§S.9), make this one of the less reliable methods of determining (/>TM' The choice

Energy Migration and Transfer 11.6

544

of a system satisfying condition (11.42) would remove process (11.13) and thus eliminate components (a) and (b), while component (c) could then be made negligible by an appropriate choice of concentrations and light intensity. 11.6 Triplet exciton migration and transfer in mixed crystals The behaviour of triplet excitons in aromatic crystals differs from that of singlet excitons (§11.4) in several important respects. (i) The triplet intermolecular interaction energy L1 WT ~ 10 cm- I in naphthalene and anthracene (§11 .3) corresponds to a triplet exciton hopping frequency (k:nigh ~ L1 WT/h ~ 3 x lOll S-I , which is a factor of ~ 10 less than the singlet exciton hopping frequency , (k:nig)M' (ii) L1 WT arises from electron-exchange interaction which is a short-range (~15 A) interaction, unlike the Coulombic interaction responsible for singlet exciton migration. Triplet exciton migration is thus more likely to be consistent with the hopping model. (iii) In the absence of triplet-triplet interactions, the unperturbed triplet exciton lifetime TT (~1 s) is determined by the rate kT (= l /TT) of the spin-forbidden TI - So decay processes, so that TT ~ 108 TM ,where TM is the singlet exciton lifetime. During its lifetime the unperturbed triplet exciton may migrate through (k'mlgh/TT ~ 3 X lOll molecules, which is a factor of ~107 more than a singlet exciton. In consequence the unperturbed triplet exciton migration length Lr ~ 100 j-tm, which IS a factor of ~ 10 3 larger than the singlet exciton migration length L M • (iv) In a pure aromatic crystal triplet-triplet interactions occur (11.15)

e

yielding singlet excitons M*) and delayed fluorescence . These interactions considerably reduce the mean lifetime TT and mean diffusion length LT of the triplet exciton. They compete efficiently with the much slower phosphorescence transition (k pT :: 0·03 S- I) so that phosphorescence is rarely observed from a pure aromatic crystal. On the other hand, the observation of the delayed fluorescence provides an important technique for the study of triplet exciton migration in pure aromatic crystals, which will be discussed in §11.8. Initial evidence for efficient triplet exciton migration in aromatic crystals came from the observation that the impurity quenching of the triplet state of crystalline naphthalene is much more efficient than that of the singlet state.75 Nieman and Robinson 54 observed triplet energy transfer between different isotopic species in three-component isotopic mixed benzene

11.6 Triplet Exciton Migration and Transfer in Mixed Crystals

545

crystals at 4·2°K . The replacement of a hydrogen atom in benzene by a deuterium atom results in a ~33 cm- 1 increase in the lowest singlet and triplet o - 0 transition energies,76 so that Es(C6D6) - Es(C6H6) ~ ET(C6D~) - ET(C 6H 6) ~ 200 cm- 1 The isotopic shift is due to a change in the zero-point vibrational energy. The other fluorescence and phosphorescence properties of the different isotopic species in a common (C6D6) host at 4·2°K are similar to each other. The phosphorescence lifetimes TT 76 are C6H3D3' 8·8 s; C 6H 4D 2 , 8·9 s; C 6HsD, 8·5 s; C 6H 6, 8·5 s; which are identical within the experimental error (± 0·3 s). The absence of an isotopic substitution effect (§5.8) on TT is surprising, since TT = 16 s for C6H6 and 26 ns for C6D6 in an argon matrix. 77 The latter is attributed to a change in kGT (§5.9), and it has been suggested 76 that the radiative transition probability kPT may be sufficiently enhanced by the crystal field that kPT ~ kGT in the crystal (cf. §6.17). Nieman and Robinson s4 studied the 4·2°K luminescence of crystals consisting of: (A): 99·2% C6D6 (M), (B): 99·2% C6D6 (M),

0·4 %C6H6 (Z)

0·4% C 6HsD (Y), 0·79% C6HSD (Y),

0·01 % C6H6 (Z)

The guest molecules C 6HsD (Y) and C6H6 (Z) function as both singlet and triplet exciton traps of depth Ll YM (= ESM - Esy = ETM - E TY ) ~ 170 cm- 1 and LlZM ~ 200 cm- 1 , respectively. Radiation is initially absorbed by the host crystal (M), and the 1 M* excitons migrate and transfer to ly* and lZ*. No IM* fluorescence or 3M* phosphorescence is observed, showing that the I M* transfer competes efficiently with I M* - 3M* intersystem crossing. 76 ly* fluoresces, transfers to lZ*, or intersystem crosses to 3y*, and lZ* fluoresces or intersystem crosses to 3Z*. 3y* phosphoresces, transfers to 3Z*, or intersystem crosses to ly, and 3Z* phosphoresces or intersystem crosses to I Z. If there were no guest-guest transfer the ratio of emission intensities from the two guests would approximate to their concentration ratio. Guest-guest transfer distorts this ratio in favour of the deepest trap. The observed fluorescence (IF) and phosphorescence (Ip) quantum intensities for the two crystals at 4·2°K were as follows: hM = IpM = O

(A): IFz /I Fy = 1·0 - 1·5; (B): IFz/IFy ~ 0;

Ipz/lpy Ipz/lpy

~

~

10

0·3

The results show conclusively that guest-guest transfer of triplet excitation occurs efficiently, while guest-guest transfer of singlet excitation is much

Energy Migration and Transfer 11.6

546

less significant. The result for crystal B, where ~O'25 of the total phosphorescence intensity is from C6H6 (Z) which is present in only ~1O-4 concentration is particularly striking. Figure 11.5 shows subsequent measurements by Colson and Robinson 76 of IFz/IFY and Ipz/lpy as a function of the guest mole fraction Cy (= cz) for this system. An analysis 76 of the tri plet-triplet energy transfer on the active sphere model (11.44) yields

1

Phosphorescence

.2

E Fluorescence _ _ _ _I

1- - 1 -1- - 1

o

02

04

06

08

10

% Concentration -

Figure 11.5 Energy transfer in benzene isotopic

mixed crystals. Equimolar solutions of C6H6CZ) and C6HSDCY) in C6D 6(M) at 4'2°K and low light intensity. Fluorescence intensity ratio (IFZ /hy) and phosphorescence intensity ratio (Ipz//py) as a function of the concentration of Y (and Z) (after Colson and Robinson 76 ) a value of R zy c:::: ] 5 A for the transfer radius, assuming the transfer to be isotropic. These triplet transfer experiments show the existence of relatively large intermolecular electron-exchange interactions in mixed isotopic benzene crystals, and they thus furnish indirect evidence for triplet exciton migration in the host crystal. The phosphorescence intensity of a pure benzene crystal is negligible, and this is attributed 78 to competing rapid triplet-triplet annihilation reSUlting from triplet exciton migration. The So - T J absorption in crystalline benzene is too weak to have yet been observed (Table 6.9), so that there are no data on the Davydov splitting of the triplet exciton

11.6 Triplet Exciton Migration and Transfer in Mixed Crystals

547

Robinson 79

states. Nieman and introduced the method of 'variation of energy denominators' as an alternative mode of determination of the nearest neighbour pair interaction matrix element f3 in crystalline benzene. They observed the phosphorescence spectra of dilute mixed crystals of C6H6 in C 6D 6, C6H3D3 and C 6H4D 2 at liquid helium temperatures. In an isotopic host the C6H6 phosphorescence spectrum is shifted by an energy

4f32 0 = JE

(11.55)

where the energy denominator JE is the difference between the 0 - 0 phosphorescence transition energies (ET ) of C6H6 and its isotopic host, and the factor 4 arises from the equivalence of the four most strongly interacting neighbours in the crystal lattice. The observed spectral shifts correspond to a value of f3 = 12 ± 1 cm- I forthe benzene crystal (see 11.3, p. 635). Direct evidence for triplet exciton migration in benzophenone crystals was obtained by Hochstrasser Bo and by Rousset and co-workers. 19B A pure benzophenone crystal emits phosphorescence only, and an intersystem crossing rate kTM c::: 1010 S-I is deduced from the 1 M* and 3M* lifetimes. The phosphorescence yield (j)PT decreases by a factor of _10 2 in raising the temperature from 77°K to 300 o K , corresponding to a decrease in the triplet lifetime TT from 6 ms to -60 p-s. A benzophenone (M)- naphthalene (Y) mixed crystal (cy = 10- 5 ), excited into 1 M *, for which (11.56) emits mainly 3y* phosphorescence «(j)py/ (j)PT c::: 20) and the quantum yield o (j)py does not decrease significantly in going from 77°K to 300 K . This shows that 3y* is excited by energy transfer either from 3M* following 3M* migration, or less probably from IM* following IM* migration. To eliminate the second possibility, a second mixed crystal system was studied, benzophenone (M)-l :2-benzanthracene (Y) with C y = 10- 4, for which (11 .57) The mixed crystal value of (j)Py/ (j)FY c::: 1 is much greater than that of (j)Py/ (j)FY ~ 10- 3 obtained for 1: 2-benzanthracene in EPA glass at 77°K , showing that the quantum efficiency of 3M* - 3y* energy transfer is much greater than that of 1 M* - 1y* energy transfer. (The alternative possibility that Iy* - 3y* intersystem crossing is enhanced in benzophenone solution was eliminated by subsidiary experiments.) Although 1 M* migration occurs with an estimated rate of k:nig - 10 12 S- I, the 1 M* - 1y* transfer rate of k:nl g Cy c::: lOB S- I is much less than the 1 M* - 3M* intersystem crossing rate of kTM c::: 10 10 S- I, so that the latter process competes strongly with energy transfer from IM* .

Energy Migration and Transfer 11.6

548

For the benzophenone-naphthalene system rJ>py

rJ>PT =

qpy(k:nigh Cy k pT

(11.58)

ifit is assumed that Iy has a unit 3M'" exciton capture probability (p = 1). Substitution of rJ>py/ rJ>PT = 20, qpy = 0·04 for naphthalene (Table 6.2), k pT ~ kT = 1·7 X 10 2 S-I for benzophenone at 77°K, and Cy = 10-5 , gives (k:nlgh '::: 7·5 x 109 S- I (benzophenone)

for the 3M* migration rate: The observation that rJ>py does not decrease significantly at 300 K shows that (k:nlgh > kT/Cy = 1·7 x 109 S-I, and a value of (k:nlgh ~ 10 10 S-I was estimated 80 from the benzophenonebenzanthracene mixed crystal data (see p. 635). The experiments discussed so far show the occurrence of: 0

(i) 3y* - 3Z* energy transfer between two guest molecules by electron exchange interaction over a distance R zy ~ 15 A, with the host crystal functioning as a solvent7 6 ; and (ii) 3M* migration in the host crystal, leading to 3M * - 3y* transfer to a guest molecule.80 Because of the long triplet excitation lifetime, a third type of triplet migration and transfer process can occur in a mixed crystal, consisting of a host (M) and low concentrations Cy, Cz of two guest species (Y, Z) such that (11.59) If 3y* is excited, 3y* - 3Z* transfer by direct electron exchange interaction (i) cannot occur if the Y - Z intermolecular separation exceeds R zy • At low temperatures no 3y* - 3Z* transfer is observed, but at higher temperatures quenching of 3y* and sensitization of 3Z*, corresponding to 3y* _ 3Z* energy transfer, is observed. This is due to: (iii) thermal activation of 3y* to a vibronic state 3y**, isoenergetic with the host triplet exciton band 3M*, leading to 3y** - 3M* transfer, 3M* migration, and 3M* - 3Z* transfer. This type of behaviour, thermally activated transfer of triplet excitation between two guest molecules via the triplet exciton band of the host crystal, was demonstrated by Hutchison and co-workers 81 - 83 using electron spin resonance to observe and distinguish the triplet species. In a typical system studied, M = biphenyl, Y = phenanthrene'd lO , and Z = naphthalene, ETM - ETY = J TMy '::: 1600 cm- I , ETY - ETZ = J TyZ '::: 300 cm - I , and (11.60)

549

11.6 Triplet Exciton Migration and Transfer in Mixed Crystals

The naphthalene (3Z*) E.S.R. spectrum was observed under conditions (11.60) where only ly* was initially excited, yielding 3y* by intersystem crossing. High precision measurements showed the absence of any environmental effects due to more than the statistical number of adjacent naphthalene-phenanthrene pairs in the crystal, showing that the 3y* - 3Z* transfer occurs through the host crystalY In further experiments82 • 84 biphenyl (M) crystals containing (A):

Cy

~ 2 X 10-3 phenanthr6ne'dlQ (Y)

(B): Cz ~ 5

(C):

Cy ~

X

2

10- 4 naphthalene (Z), or X

10-3 and

Cz ~

5

X

10- 4

were irradiated with light from a high pressure Hg arc (i.e. both Y and Z were excited) until photostationary conditions were established. The irradiation was then terminated and the decays of the 3y* and 3Z* E.S.R. signals were observed. From 4°K to ~80 oK the decays are exponential, with mean lifetimes of TTY = 10·0 sand TTZ = 2·2 s, respectively. The observations at higher temperatures are shown in Figure 11.6. On increase of the temperature from 85°K to 120oK, the 3y* decay in crystal A deviates from exponential behaviour and decreases towards zero. The solid curves (Figure 11.6) show the time for the first lie of the signal to decay. This behaviour is attributed to thermal activation of 3y* through the energy gap Ll TMy to 3y**, isoenergetic with 3M*, leading to 3y** - 3M* transfer, 3 M* migration, and culminating in heteropolar triplet-triplet association, by a process such as (l1.18b) A kinetic analysis, assuming (l1.18b), is quantitatively consistent with the results 83 , although other heteropolar triplet-triplet association processes are also possible (§ 11. 7). The 3Z* decay in crystal B behaves in a similar manner, but at rather higher temperatures, because of the increased energy gap Ll TMZ ' The addition of Cz ~ 5 X 10- 4 to crystal A to form the ternary crystal C has a dramatic effect on the behaviour (Figure 11.6). At 100 K the 3y* lie decay time is decreased from ~9 s to ~5 s, and the 3Z* lie decay time is increased from ~2 s to ~5 s. This behaviour is due to the additional energy transfer process 0

(ll.lla) which competes with process (11.18b) for the 3 M* excitons produced by thermal activation of 3y*. A kinetic analysis agrees quantitatively with this description, and the activation energy for the overall 3y* - 3Z* energy

550

Energy Migration and Transfer 11.7

transfer process agrees closely with Ll TMy , confirming that 3M* exciton migration is involved as an intermediate process. HirotaS4 has extended these experiments to a variety of similar systems, utilizing deuteration of the guest and host to study the effect of the resultant energy level shifts on the triplet decay (§I1.7). A further example of this

10 ''-,

,

A (y)

C (y )\

8

\

\

\ \ \

/ I

4

C( Z ) / -'

..-\\ ' \ \

\

\

\

--

2

~

\

B(Z)

\ \

"

O L-~~~__~~-L__~__~__~~~~

80

100

12 0 T (deg K )

140

15 0

Figure 11.6 Triplet-triplet energy transfer in mixed crystals of biphenyl (M) containing phenanthrene'd lO (Y) and/or naphthalene (Z) . Triplet decay time (TT) as a function of absolute temperature (T). Crystal A, M + 2 X 10- 3 Y; crystal B, M + 5 X 10- 4 Z; crystal C, M + 2 X 10- 3 Y + 5 X 10- 4 Z (after Hirota and Hutchison 82 • 8 4 ) type of behaviour is shown in Figure 11.7, which plots the E.S.R. ey*) signal in tensi ty under co nstan t ill uminati 0 n of 2-meth yIna phthalene·d 10 (Y) in naphthalene and in naphthalene·d s as a function of temperature. S3 The 3y* quenching with increase in temperature is due to thermal activation through Ll TMy , 3y** - 3M* transfer, 3M'" migration, and 3M* _ 3y* association (II.I8b), as in crystals A and B. The energy gaps of Ll TMy ~ 140 cm- I for the naphthalene host and Ll TMy ~ 270 cm- I for the naphthalene·d s host are consistent with the observed behaviour (Figure 11.7). 11.7 Triplet-triplet interactions in mixed crystals A 'pure' organic crystal contains a small concentration [I X] of trapping centres, due to defects or residual impurities, which have a triplet excitation energy E rx lying below the triplet exciton energy ETM of the host crystal

551

11.7 Triplet-Triplet Interactions in Mixed Crystals

M. At low temperatures where the thermal energy kT is less than the trap depth, (11.61) Ll TMX = ETM - E TX these function as traps for the free triplet excitons 3M *. Such trapped

9

-fftt\,~

8

I

10

,B-Methylnaphthalene-

0

dlo in naphthalene-ds

Q

1

7

\

!t \ f

4

1

\" ,B-Methylnaphthalene -

~

\

dlo in naphthalene

g

Q

\ Q\ Q

Q\

3

~

2

Q

\

o~ O~~~~~~~~~~~~~~ 8

10

12

14

16

18

20

T (OK)

Figure 11.7 Magnetic resonance signal intensities with constant illumination (oc triplet concentration) of 2-methylnaphthalene·d lO in naphthalene and naphthalene·d s as a function of temperature (after Hutchison S3 )

triplet excitons will be referred to as 3X*. The dynamic equilibrium between 3M* and 3X* (11.62) depends on LlTMX/kT and the molar concentrations of the different species. Provided [3M*] < [IX], i.e. there is no trap saturation, the relative concentrations of trapped and free excitons are [3X*] [IX] [3M*] ~ [IM)exp(Ll TM X/kT)

(11.63)

552

Energy Migration and Transfer 11.7

At high temperatures (LlTMX > kT), the majority of the excitons are in the free state 3M*, since [I M] > [IX], but at low temperatures (LlTMX < kT) the fraction of trapped excitons becomes significant. The addition of a guest species Y, whose triplet excitation energy ETY (= ETM - LlTMY) lies below ETM and E TX , to the host crystal introduces guest traps for the triplet excitons, and such guest-trapped excitons will be referred to as 3y*. The dynamic equilibrium between 3M* and 3y* (16.64) depends on Ll TM y/kT and the molar concentrations of the different species. Provided [IY] > [IX], [3M*], i.e. traps are unimportant and guest saturation does not occur, the relative concentrations of guest and free excitons are [Iy] [3y*] [3M*] ~ [1M] exp (Ll TM y/kT)

(11.65)

Figures 11.6 and 11.7 illustrate the manner in which [3y*] decreases with increase in temperature. A binary mixed crystal exhibits two types of delayed emission, phosphorescence and delayed fluorescence, the latter resulting from thermally activated triplet-triplet annihilation, which competes with the phosphorescence. 78 McGlynn et al. B5 have distinguished three types of triplet-triplet annihilation process, which can occur in mixed crystals initially excited into IM*. In this case 3X* and 3y* are populated either by 1M'" migration and transfer to IX'" and Iy*, followed by intersystem crossing to 3X* and 3y*, or by IM* intersystem crossing to 3M*, followed by 3M* migration and transfer to 3X* and 3y*. (i) Guest-guest annihilation (l1.66a) 3 y** + IM~ly + 3M* 3 M*+3y *~ IM+ly*

(11.66b) (l1.18b)

(ii) Guest-trap annihilation (1 1. 67a) 3X* * + 1M

~

IX+ 3M*

3M*+3y*~IM+ly*

(l1.67b) (lU8b)

(iii) Trap-trap annihilation Processes (1 1. 67a) and (11.67b) leading to 3 M* +3 X* ~ IM +I X*

(lU8d)

11.7 Triplet-Triplet Interactions in Mixed Crystals

553

On the McGlynn terminology, in which A - B annihilation refers to the association of a triplet originating from B with a second triplet A, there are several other possible processes to be considered. (iv) Trap-guest annihilation Processes (l1.66a) and (11.66b) leading to (ll.lSd). (v) Host-guest annihilation Processes (l1.66a) and (11.66b) leading to 3M*

+ 3M* --+ 1M + IM*

(l1.15)

(vi) Host-trap annihilation Processes (l1.67a) and (l1.67b) leading to (11 .15). (vii) Guest-host annihilation Process (ll.lSb). (viii) Trap-host annihilation Process (1l.lSd). (ix) Host-host annihilation Process (11.15). Processes (i), (iv) and (v), which have an activation energy of Ll T My , will occur at higher temperatures. Processes (ii), (iii) and (vi), which have a lower activation energy of Ll TMX , will occur at lower temperatures. Processes (vii), (viii) a nd (ix) are initiated by free eM*) excitons and have a negligible activation energy. They are important in pure crystals (§I1.S) or in mixed crystals at high excitation intensities, where guest and trap saturation occur. Processes (i), (ii) and (vii) yield guest ey* ) delayed fluorescence ; processes (iii), (iv) and (viii) yield trap eX*) delayed fluorescence; and processes (v), (vi) and (ix) yield host eM*) delayed fluorescence. The processes 3M* + 3y * --+ IM* + Iy (lUSc) 3M*

+ 3X* --+

IM*

+ IX

(ll.lSe)

are possible alternatives to (l1.ISb) and (l1.ISd), respectively, which would yield 1M * delayed fluorescence . This type of heteropolar triplet-triplet annihilation process in which the partner M*) with the higher singlet excitation energy is excited might possibly be observed in fluid solution, but not in crystals, since the I M* excitation energy is rapidly transferred to Iy* or IX*, respectively, by (11.10) or (11.13). Hence in a heteropolar triplet-triplet annihilation process in a mixed crystal, the delayed fluorescence is characteristic of the partner with the lower singlet excitation

e

Energy Migration and Transfer 11.7

554

energy. There are other possible triplet-triplet interaction processes of the type (11.20) which do not yield delayed fluorescence. The relative importance of processes (i)-(ix) in a given system depends on several factors: (a) the mode of excitation, (b) the sequence of the singlet and triplet energy levels of M, X and Y, (c) the energy gaps Ll TMy and Ll TMX , (d) the temperature, (e) the mole fractions Cy (=pY]/ PM]) and Cx (= PX]/ PM]) of guests and traps, respectively, and (f) the intensity and period of excitation. McGlynn et al. 85 investigated the delayed fluorescence from various binary crystal systems for which, (11.68) In all cases delayed fluorescence was observed only from the guest species Y, showing that for these systems under the particular experimental conditions (low excitation intensity, temperature from 77°K to 2700K) only the annihilation processes (i) and (ii) are significant. For the guest-guest annihilation process (i) the delayed Iy* fluorescence intensity Ity and the 3y* phosphorescence intensity Ipy are related by85 .

Ity [,2 py

oc

k Fy [3M*] [3Y*] , k 2 [3y*y = Kyy exp (- Ll TM yJkT) py

(I 1.69)

Similarly, for the guest-trap annihilation process (ii),

~~y = K~x exp (-LlTMx/kT) py

(I 1.70)

Figure 11 .8 plots observations 85 ofthe temperature dependence of Ity and fpy for mixed crystals of naphthalene, naphthalene·d 8, phenanthrene, and chrysene in biphenyl. Figure 11.9 shows typical plots oflog(lty/fiy) against l i T for (a) phenanthrene·d lo in biphenyl,82 and (b) phenanthrene in biphenyl. 85 The behaviour in the high- and low-temperature regions is consistent with (11.69) and (11.70), respectively. Table 11.8 lists the experimental values of Ll TMy and Ll TMX thus obtained for various binary crystals. The values of Ll TMy agree satisfactorily with the spectroscopic energy gaps (ETM - E TY ) obtained from the phosphorescence spectra, confirming that the guest-guest annihilation (i) involves thermal activation into the 3M* exciton band. The values of Ll TMX represent average trap depths and are relatively large because of the multicrystallinity of the specimens.

11.7 Triplet-Triplet Interactions in Mixed Crystals

555

Studies of the same systems under the condition ESM > Esx > Eex > Esy > ETM > E TX > E Ty

(11.68a)

would be of interest, since this would eliminate the initial excitation of 3X* Naphthalene - ds in biphenyl

Naphthalene in biphenyl

\

\

Chrysene in biphenyl

Phenanthrene in biphenyl

\

•\

.,

•,

\

60

100

140

180

220

260

Temperature in OK ------+--

Figure 11.8 Temperature dependence of delayed fluorescence intensity (solid lines) and phosphorescence intensity (broken lines) of mixed crystals of different guests in biphenyl hosts (after McGlynn, Misra and McCoy85) and thus inhibit the guest-trap annihilation process (ii). Similar studies of a binary system satisfying the condition (11.71) should modify the heteropolar triplet-triplet annihilation process from

(lU8b) to (11.18c)

556

Energy Migration and Transfer 11.7

co-workers 85 - 9o

McGlynn and have made a series of studies of the phosphorescence and delayed fluorescence spectra, intensities and decay functions of various binary crystals as a function of temperature from 77°K upwards. The results are generally consistent with the guest-guest (i) and guest-trap (ii) annihilation processes, and the reaction kinetics are similar to those for delayed fluorescence and phosphorescence in fluid solutions described in Chapter 8. For melt-grown crystals of biphenyl containing a 4 0.------,------r-- - , - -----,

4 0 30

I

(1850 ±150)cm- 1 30 2.0 +- S cale a 2 ·0

"-."0'

0'

52

1

>-

No. ~ >-

52

1·0

10 (350 ± 50) cm- 1 0 50 10'l'TinoK - 1 _

Figure 11.9 Plot of 10gU:ylI;y) against reciprocal temperature, l i T. (a) phenanthrene'd lO

in biphenyl,82 (b) phenanthrene in biphenyl (after McGlynn, Misra and McCoy85) relatively high mole fraction (c y = 6 x 10-3 ) of pyrene, they observed 88 a weak delayed fluorescence characteristic of the pyrene excimer, in addition to the delayed pyrene molecular fluorescence, and in some melt-grown crystals oflower pyrene concentration (c y = 10-4 ) they observed vibrational structure in the excimer spectral region. The delayed molecular and excimer fluorescence have identical lifetimes and excitation spectra and their intensities depend in the same manner on temperature and on the incident light intensity. Both emissions are considered 88 to originate from guest-trap annihilation (ii), from an unidentified trap or residual impurity. Similar mixed crystals grown by sublimation exhibit delayed pyrene molecular fluorescence, but no prompt or delayed excimer fluorescence, indicating that the excimer fluorescence from the melt-grown crystals is due to molecular aggregates. Detailed studies of the delayed fluorescence of mixed

11.7 Triplet-Triplet Interactions in Mixed Crystals

557

crystals of anthracene in naphthalene, anthracene in phenanthrene, and tetracene in anthracene have been made by Rousset. 19 9 Similar studies of triplet-triplet interactions in binary and ternary mixed crystals have been made by Hirota and Hutchison,s2-s4 using E.S.R., phosphorescence and delayed fluorescence intensities to study the time, temperature and concentration dependence of the excited triplet species. Typical results are shown in Figures 11.6 and 11.7 and have been discussed in §11.6. The triplet-triplet ey* - 3Z*) energy transfer involves the following sequence of processes (1 1. 66a) 3 y * *+lM ~ ly + 3M*

(11.66b)

3M* + lZ ~ IM + 3Z*

(1 l.l la)

Hirota S4 has determined the thermal activation energy Ll TMy for the overall process, which agrees closely with the spectroscopic energy gap (ETM - ETY ), and also the rate k TMy PM] of process (11.66b). His results, which are listed in Table 11.9, confirm the mechanism (see p. 635). Port and W 0lf5 5 have studied the temperature dependence from 1·6°K to 400K of the phosphorescence and delayed fluorescence spectra and intensities of single crystals of naphthalene and naphthalene·d s containing various guest molecules. Figure 11.10 shows the temperature dependence of the phosphorescence intensity (lpy) and delayed fluorescence intensity (lty) of 10- 3 2-methylnaphthalene (Y) in naphthalene. The plot of log (Itylliy ) against I IT is consistent with (11.69), and the value of Ll TMy = 240 ± 40 cm- I agrees with the spectroscopic energy gap, ETM - ETY = 240 cm- I . The delayed fluorescence is due to guest-guest annihilation (i). Impurity molecules, like thionaphthene, in naphthalene do not act as direct traps for singlet excitons, but naphthalene molecules near these impurities are disturbed so that they become shallow X-traps,35 and the crystal fluorescence spectrum is red-shifted by the trap depth LIE (§I1.4). In a similar manner, thionaphthene and durene (ex ~ 10- 4) create X-traps for triplet excitons in naphthalene, and cause a red-shift LlET of the naphthalene phosphorescence spectrum. 55 Figure 11.11 shows the temperature dependence of the X-trap phosphorescence intensity (lpx) and delayed fluorescence intensity (ltx) of thionaphthene (ex = 10-4) in naphthalene. The plot of log(ltxllix) against l iT yields an activation energy Ll TMX = 42cm- l , in agreement with the spectroscopic value of LlET = 45 cm- I . Durene (ex = 10- 4 ) in naphthalene gives Ll TMX = 50 cm- I , LlET = 60 cm- I • The delayed fluorescence is thus due to the trap-trap triplet annihilation process (iii).

Energy Migration and Transfer 11.7

558

An unidentified triplet X-trap is observed 55 in the purest crystals of naphthalene'd s which causes a red-shift of LlET = 40 cm- I in the phosphorescence spectrum at T < 2'5°K , and which at T> 2'5°K is thermally depopulated with an activation energy Ll TMX = 40 em- I. The behaviour of T (OK)

25

50

15

10

7

8

7

4 p

5

i~'-'-'-'-'-~-"--

3

. •

2

;,.

•

:;.

.;"

3

.•,

....

~

I·

•

.;

• / •

2

• \

I

20

40

60

80

--.~~

100

120

o

14 0

( 1/ T) xI0 3

Figure 11.10 Phosphorescence intensity lpy and delayed fluorescence intensity lty (right-hand ordinates) and ratio (f:y/l~y) (left-hand ordinates) versus reciprocal temperature for crystal of 10- 3 2-methylnaphthalene in naphthalene (after Port and Wolf 55)

crystals of naphthalene'd s (ETM = 21,310 em-I) containing 0·02 naphthalene'h s (ETY = 21,210 em- I) is influenced by these X-traps (ETX = 21,270 em-I). The plot of 10g(l#yIIJy) against liT yields an activation energy Ll = 60 em- I, which is less than (ETM - E TY ), but which corresponds to (ETX - ETY)' It is suggested 55 that in this system the guest-guest triplettriplet annihilation occurs via the 21,270 cm- I trap as an intermediate: (ll.72a)

559

11.8 Triplet Excitons in Pure Crystals

3X*

+ Ll TMX + 1M --+ IX + 3M* + 3y* --+ 1M + Iy*

(ll.72b)

3M*

(1 USb)

the second step (ll.72b) occurring rapidly, since Ll TMX < Ll TMy • The first step (\ l.72a), which involves energy transfer by exchange-interaction, T (OK)

25

3

4

2

16

5

3

4

~ ..,>-

P

......

3

.

/ .. .:.....~\

~ 0>

~

2

AA_A............... _A_ ... _ A -

,"

• / I"

f'

..

'. •

/

\. •

/

/ '.

..

/

\0

\

300

...............

•

DF e_

0

..i 0 0

............

0

0

0

o

0

00

400

500

600

1fT (x 10 3 )

Figure 11.11 I py , I:y and I:y jliy versus reciprocal tem-

perature for naphthalene crystal containing thionaphthene X-traps (after Port and Wolf 55 ) would appear more likely if the X-traps are directly associated with the guest (Y) molecules, rather than characteristic of the 'pure' host crystal (M). 11.8 Triplet excitons in pure crystals The study of triplet excitons in pure aromatic crystals has been facilitated by two phenomena discovered 91 in 1963: (a) triplet-triplet eM* - 3M*) annihilation yielding delayed IM* fluorescence (11.15) as proposed by Sternlicht et al.78;

Energy Migration and Transfer 11.8

560

(b) direct singlet-triplet eM - 3M*) excitation by red light from a ruby laser or other intense source. Most studies have been concerned with anthracene crystals, usually at room temperature, and Avakian and Merrifield 92 have reviewed the literature up to the end of 1967. At room temperature the triplet excitons eM* ) are essentially free, although trapping at defects and residual impurity sites occurs at lower temperatures. The concentration n (= N' [3M*D of free triplet excitons per unit volume at position x and time t in a crystal is governed by the rate equation 93 - 94

atan = IXI.-

f3n - yn 2 + D\1 2n

(11.73)

where IX is the So - T J absorption coefficient (cm- I ) for the incident 'red' photon flux i, f3 (= kT) is the unimolecular triplet decay rate, y (= kTT) is the total triplet-triplet annihilation rate parameter, and D (= .lh) is the triplet diffusion (migration) coefficient. The intensity of delayed fluorescence per unit volume is given by rp

=

1-Yrad n 2 =

-t fyn 2

(11.74)

and the total emitted delayed fluorescence from the crystal is (p

I

= 1- fy n 2 d V

(11.75)

volume

wheref = Yrad/Y (=qFMkMTT/kTT) is the fraction oPM* - 3M* annihilations which lead to delayed fluorescence. The symbols of(lI.73)-(11.75) are those in general usage, althoughfwas commonly equated to unity in the earlier work. Triplet excitons can be generated directly in an anthracene crystal by a pulsed ruby laser,91 an intense xenon arc 95 or a helium-neon laser. 96 A value of IX = 10-5/ fcm- I has been obtained for the So - T J absorption coefficient for ruby laser light at ,\ = 694·3 nm , from a comparison of the number of incident red photons and the number of emitted blue photons per unit thickness under conditions where triplet-triplet annihilation was dominant. 9J The So - T J absorption spectrum was obtained from the delayed fluorescence excitation spectrum [§6.8 (iv), Figure 6.5] observed with a xenon arc and monochromator. 95 At wavenumber ii the photo stationary solution of (11.73) and (11.74) with uniform illumination (\1 2 n = 0) and low 3M* concentration (f3n ~ yn 2 ) reduces to rp(ii)

= ! fy IX2(ii~!2(ii)

(11.76)

11.8 Triplet Excitons in Pure Crystals

561

so that cp(JJ)li (ii) is proportional to the square of the absorption coefficient cc(ii). Normalization to the ruby laser value of cc gives a maximum of cc = 3·4 x 10-41jcm- I at,\ = 620 nm. At low light intensities (f3n > yn 2 ) , cp is proportional to i 2 (11.76). At high light intensities, where yn 2 > f3n, (11. 73) and (11. 74) reduce to 2

cp = t jrJ.i

(11. 77)

In general (11. 78)

The decrease of p from 2 at low i towards 1 at high i has been shown experimentally using a 100 mW helium-neon laser (,\ = 632'8 nm).92 Triplet excitons can also be generated in anthracene crystals by other methods. (i) So - SI absorption leads to intersystem crossing to the triplet manifold. In the anthracene molecule in solution, T2 lies -800 cm- I below SI (§6.l0), so that even at low temperatures SI - T2 intersystem crossing (k~M = 11 X 10 7 S-I) competes efficiently with SI - So fluorescence 7 (kFM = 6 X 10 S- I). In the anthracene crystal, exciton interaction, which affects the singlet states more than the triplet states (§11.3), reduces the SI energy below that of T 2, so that the SI - T2 intersystem crossing requires thermal activation. From the decrease in the delayed fluorescence intensity, excited via Sj, with decrease in temperature, Adolph and Williams 97 have concluded that intersystem crossing in crystal anthracene has an activation energy of WTM = 800 ± 50 cm- I. (ii) Double-photon absorption into SI is a process (§3.11) which can compete with direct So - TI absorption, under intense laser excitation. It results mainly in prompt fluorescence, whose intensity is proportional to the square of the incident light intensity. This was initially confused with the delayed fluorescence, resulting from direct triplet excitation and triplet-triplet annihilation, whose intensity is also proportional to i 2 (11.76), but lifetime observations resolved the two emissions (§3.11). Apart from the prompt fluorescence, there is a small component of delayed fluorescence, resulting from double-photon absorption, intersystem crossing and triplet-triplet annihilation, which is proportional to the fourth power of the incident laser intensity.98 The integrated delayed fluorescence intensity from double-photon excitation is observed 98 to be 0·01 of the integrated prompt fluorescence intensity for crystal anthracene at room temperature. This corresponds to an intersystem crossing rate of kTM = 0·02k FM l j or, taking kFM = 9 X 10 7 s- I,29 to kTM = 1·8 X 1061j S- I. A similar value of kTM = 2·0 (±0·4) x 10 61j S-I has been obtained 99 from observations of blue-excited delayed fluorescence in anthracene crystals at room temperature.

562

Energy Migration and Transfer 11.8

(iii) Ionizing radiation represents an efficient method of generating triplet excitons. 1oo An ionizing particle passing through an anthracene crystal produces singlet and triplet excitons along its track by direct excitation, by excitation by slow electrons (o-rays), and by recombination between molecular ions and electrons. 1 These undergo internal conversion to 1M* and 3M*, which migrate away from the primary ionization column. The 1M* fluorescence yields the prompt scintillation component, and the 3M* - 3M* annihilation produces delayed 1M* fluorescence which constitutes the slow scintillation component. The intensity L of the prompt component depends on the particle energy E and also on the specific energy loss dE /dx, the differential scintillation efficiency being given by the relation/ol dL S (11. 79) dE 1 + kB(dE/dr)

S is the scintillation efficiency for particles of low dE /dr (fast electrons), and kB(dE/dr) describes the ionization quenching of the singlet excitation. Due to the ionization quenching the relative fast scintillation intensities of an anthracene crystal to a 1 MeV electron, proton and ex-particle are L = 1000, 230 and 60, respectively. 1 The intensity of the slow scintillation component Ls is much less sensitive to ionization quenching, so that Ls 'C: SsE is reasonably independent of the nature of the particle. 63 The relative intensity L /Ls of the fast and slow scintillation components thus depends on the nature of the ionizing particle, and this forms the basis for the pulse shape discrimination technique which is used to distinguish the scintillations arising from different types of ionizing radiations (e.g. y-rays which give Compton electrons, and neutrons which give recoil protons).I . 205 King and Voltz 102 have developed a quantitative theory of the slow scintillation component, which accounts satisfactorily for the observed form of the scintillation decay over several decades of intensity, in terms of an initial distribution of 3M* excitons along the track of the ionizing particle, and the subsequent 3M* migration and 3M* - 3M* annihilation yielding delayed IM* fluorescence. The migration of a free 3M * exciton may be terminated by (i) unimolecular decay, by TI - So phosphorescence (k pT) or TI - So intersystem crossing (k GT ) , with an overall rate of (3 (= k T ); (ii) 3M* - 3M* annihilation, with an overall rate parameter y (= k TT ), of which a fractionfyield delayed IM* fluorescence; o~ (iii) capture or interaction with a defect or impurity trap.

In vapour-grown crystals of high purity the effect of traps can be neglected at room temperature. 92 The phosphorescence quantum efficiency qPT is low (k pT - 1M transitions correspond to the donor fluorescence spectrum FM(ii), and occur into the various vibrational levels of IM. The possible Iy -i>- Iy* transitions correspond to the acceptor absorption spectrum Ey(ii), and occur into the various vibrational levels of IY*. The energy transfer process (11.13) is adiabatic, the difference (ESM - Esy) in the electronic energy of I M* and Iy* being partitioned as vibrational energy between the two final species 1M and Iy*. Normally the transfer is slow compared to the vibrational relaxation, corresponding to weak intermolecular coupling, so that process (11.13) is irreversible and can be described by time dependent perturbation theory.121 The energy transfer probability k~M depends on the overlap of FM(ii) and Ey(ii),

f FM(ii) Ey(ii) dii 00

k YM

ex J

=

o

(11.82)

568

Energy Migration and Transfer 11.9

since this determines the density ofisoenergetic IM* -+ 1M and Iy -+ Iy* transitions. The relation between intramolecular and intermolecular radiationless transitions has been discussed by Robinson and Frosch.1 21 In the weak coupling limit k'

- 47TPE f32 F

YM -

----..-

el

(I 1.83)

where PE is the vibronic state density, f3el is the electronic interaction matrix element between the initial and final states, and F is the vibrational overlap integral (Franck-Condon factor) given by (I 1.84)

where ifJM *, ifJM , ifJy • and ifJy are the vibrational wavefunctions of IM*, 1M, Iy* and Iy, respectively, and PEF is related to the spectral overlap integral J (I 1.82). There is a close similarity between (I1.83) and the corresponding equation (5.17) for an intramolecular radiationless transition. The total electrostatic interaction between IM* and Iy, which couples the initial and final states of (11.13), may be partitioned into Coulombic and electron-exchange terms.69 The Coulombic interaction can be expressed as a multi pole-multi pole expansion, the leading term of which is dipole-dipole (D-D). This term represents the interaction between the IM* -+ 1M and Iy -+ Iy* transition dipole moments, MM and My, respectively, so that (11.85) IMMI2 and IMyl2 are proportional to the oscillator strengths of the two transitions. The electron-exchange interaction requires overlap of the electronic wavefunctions of IM* and Iy, and it is therefore of short range (,,;;15 A). Its magnitude is proportional to J, but it is not related to the optical properties of 1M and Iy, and it leads to a relation of the form of (1 1.47). The exchange term is usually dominant at close approach of IM* and Iy,69 and if the virtual transitions in the donor and acceptor are spinforbidden, so that the Coulombic interaction is negligible, it provides the mechanism for short-range energy transfer (§l 1.5). The theory of dipole-dipole energy transfer has been developed by Forster. 122 Combining (11.82)-(11.85) and expressing the parameters in terms of experimental quantities, Forster derived the relation

(11.86)

569

11.9 Singlet-Singlet Energy Transfer in Solution

where n is the solvent refractive index, TM is the 1 M* fluorescence lifetime in the absence of Y, co

ct>FM

=

JFM(V) dv

(4.1a)

°

and €y(v) is the molar decadic extinction coefficient of 1y. K is an orientation factor, (11.87) K = cos CPYM - 3 cos CPM cos CPY where CPYM is the angle between the transition moment vectors My and MM, and CPM and CPY are the angles between these vectors and the direction M -'>' Y. The average value for a random directional distribution is K2 =-t. Equation (11.86) can be written in the form

' -_ - 1 (Ro)6 k YM

(11 .88)

r

TM

where Ro is the critical transfer distance at which energy transfer (11 .13) and 1 M* deactivation by fluorescence or internal quenching (or other means) are of equal probability. Combining (11.86) and (I 1.88) one obtains

J , IM + 1y* 1M* + 3y*

-'>'

1M + 3y**

3M* + 1y -'>' 1M + 1y* 3M* + 3y*

-'>'

1M + 3y**

(11.13) (11.22) (11.14) (11.20)

Dexter 69 has extended the Forster analysis to higher muItipole-multipole and electron-exchange interactions. The dipole-quadrupole interaction is proportional to r- 8 , and higher multipole-muItipole interactions decrease as higher inverse powers of the intermolecular separation r. These interactions are thus of shorter range than the dipole-dipole interaction, but they become important when the latter is symmetry-forbidden, e.g. in

570

Energy Migration and Transfer 11.9

benzene where the octupole-octupole interaction is dominant. 8 When the donor and acceptor transitions are spin-forbidden, electron-exchange interaction is dominant. So far we have only considered energy transfer between two isolated stationary molecules IM* and Iy. F6rster l22 and Galanin l23 extended the treatment of dipole-dipole transfer to a solution in which the two molecular species M and Yare distributed at random. They considered a solution of sufficiently high viscosity that the diffusion length V2D'TM «:: R o, so that the molecules remain efficiently stationary during the transfer process, but in which Brownian molecular rotation is much faster than the transfer rate, so that the average value of the orientation factor K2 = t can be used. For a similar solution oflow viscosity (Ro «:: V2D'TM), the energy transfer obeys Stern- Volmer kinetics, so that the transfer rate k YM pY] is timeindependent. For o-function excitation of [I M*]o at t = 0, the rate equations t> 0 are dPM*] = -(kM dt

d[~~*] =

+ k yM [1Y]) [1M*]

k yM [1Y] [IM*] - k y [1Y*]

(11.90) (11.91)

Under these conditions the fluorescence response functions (§4.4) of IM* and of Iy*, for excitation by energy transfer from IM*, are respectively, I24 iM(t) . lYM(t)

=

=

k FM [1 M*] exp {-(kM

+ k yM [1 Y]) t}

(11.92)

k Fy k yM [1Y] [1M*]o I (kM-ky) {exp(-kyt)-exp(-(kM+kyM [ Y])t)}

(11.93) These relations are applicable when the rate of statistical mixing due to diffusion and/or migration exceeds the energy transfer rate, so that k YM is effectively constant, due to 'molecular mixing'. For a solution of high viscosity (Ro ;p V2D'TM.) the molecular mixing is negligible, and since the transfer rate k~M depends on ,-6, the transfer rate is time-dependent, and the system is said to obey Forster kinetics. For o-function excitation of [1M*]o at t = 0, the rate equations at t > 0 are l24

d[1!,:*]

=

-(kM

+ yk!e t 1/2) [1 M*]

(11.94)

d[ly*] = yk~P t l / 2 [1M*] - k y [1Y*] (11.95) dt where the time-dependent rate yk~P t 1/2 replaces the time-independent rate k yM [1Y] of (11.90) and (11.91). The parameter y

=

pY]/[1Y]o

(11.96)

11.9 Singlet-Singlet Energy Transfer in Solution

571

is the molar concentration expressed relative to the critical molar concentration [iY]o of the acceptor, defined by 1 3000 [ Y]o = 2173 /2 NR6 (11.97) Solution of (11.94) and (11.95) yields the fluorescence response functions of 1 M* and of IY*, for excitation by energy transfer from IM*, which are respectively123-124

iM(t) iyM(t)

=

=

kFM[1 M*]oexp (- kM t) exp (-2y(kM t)1 /2)

kFy[i M*]o 17 1/2m em2{erf(aI /2 t 1/2 + m) - erfm}

(11.98)

(11.99)

where

a = k M-ky

m = (kM/a) I 12y and m

erfm =217- 1/2

J exp (-x 2) dx

(11.100)

o

is the error integral. For large y, (11.99) approximates to

iyM(t) ~ kFy[i M*]o {exp (-k y t) - exp (- kM t) exp (-2y(k Mt)1 /2)} (1UOI) The quantum efficiency of radiationless dipole-dipole transfer from 1 M* to Iy*, obeying Forster kinetics, is given byl22

fYM

=

17 1/2 Y exp (y2)(1 - erfy)

(11.102)

which, for large y, approximates to

fYM ~ 1-!y2

(11.103)

This differs from the corresponding relation for a system obeying SternVolmer kinetics, for which kyM[iY] fYM = kM + kyM[iY] (11.104) Irrespective of the kinetics, in the presence of [i Y] the 1 M* fluorescence quantum yield is reduced from ( v'2D'TM' The condition Ro> v'2D'TM can also be satisfied in

576

Energy Migration and Transfer 11.10

solvents of normal viscosity (e.g. toluene, D = DM + Dy :::: 4 x 10-5 cm 2 S-I), provided Ro is large (~50 A) and TM is small (~l ns). It is common practice 1 to add a secondary solute 1Z to a binary liquid scintillator solution, consisting of the solvent 1 M and a primary solute 1Y. Solvent-solute energy transfer from 1 M* to 1y* occurs through 1 M* migration and transfer as discussed in §11.11. The addition of [lZ] (~0·1 [lY]) introduces a small component (~10%) of direct IM* to IZ* transfer, but the main effect is the introduction of Iy* to IZ* transfer, which occurs both radiatively and radiationlessly by dipole-dipole interaction. Figure 11.1 shows the results of such a study2 of solute-solute transfer from p-terphenyl to TPB in toluene solution. Because of the short lifetime (Ty = 1·3 ns) of p-terphenyl, and the large donor-acceptor spectral overlap (11.82), Ro> V2DTy. The value of Ro determined from fNR as a function of PZ] agrees reasonably with that evaluated from the spectroscopic data (11.89). Terskoi et al. 209 have critically reviewed other experimental tests of the Forster theory. The electron-exchange and higher multipole-multipole interactions are proportional to r-n , where n > 6. The resultant kinetics and the theoretical dependence offYM and iM(t) on the acceptor concentration pY] differ from Forster dipole-dipole interaction kinetics. These have been considered by Dexter 69 and by Inokuti and Hirayama. 135 In the limit as n ~ 00, the short-range interaction is reasonably approximated by a 'hard-core potential' of radius R, corresponding to the 'active sphere' model (11.107) (§9.11). Thus the form of the pY] dependence of iYM for n> 6 is expected to be intermediate between the Forster kinetic case (1) and the 'active sphere' case (2) (Figure 11.12). 11.10 Influence of diffusion on energy transfer

In §11.9 we discussed singlet-singlet energy transfer in solutions in which the molecules are either stationary, or the diffusion or donor excitation migration are sufficiently small that v2DTM or v2ATM ~ Ro. Under these conditions dipole-dipole transfer is described by Forster kinetics. We now consider dipole-dipole transfer in a low-viscosity solution of 1M and Iy in which v2DTM ~ R o, so that efficient molecular mixing occurs: the energy transfer obeys Stern-Volmer kinetics and is described by a time-independent parameter k yM. The effective critical transfer distance (RO)eff under these conditions, which can be evaluated from observations of fYM against [lY], using (11.108) and (11.97), exceeds the value Ro for transfer between stationary molecules. The [l Y] dependence of the radiationless component fNR of fYM, which is described by (11.1 04), has been verified by several observers. Care is

11.10 Influence of Diffusion on Energy Transfer

577

necessary in such measurements to allow for the effect of the radiative transfer component,jR (11.25) (cf. Figure 11.1). One means of eliminating or reducingiR is to use a donor eM) with a negligible fluorescence quantum yield, and an acceptor ey) of high fluorescence quantum yield. This method was used by Bowen and Brocklehurst,136 who thus demonstrated radiationless dipole-dipole transfer from l-chloroanthracene eM) to perylene ey) in the absence of radiative transfer. The [lY) dependence of the fluorescence response functions iM(t) and iyM(t), which are given by (11.92) and (11.93), has been observed by Birks et al. 137 for anthracene eM) and perylene e Y) in deoxygenated benzene solutions, using the phase and modulation fluorometer (§4.6). The diffusional molecular mixing increases the critical transfer distance from Ro = 31 A (for stationary molecules) to (RO)eff = 43 A. The shapes of iM(t) and iyM(t) depend only on the radiationless transfer component, and they are unaffected by any parallel radiative transfer. The method is therefore suitable for determining k YM in a system in which radiative transfer is present. The influence of diffusion on dipole-dipole energy transfer has been treated theoretically by several authors. The various approaches may be divided into two broad groups: (a) those of Kurskii and Selivaneko,138 Samson,139 Bagdasaryan and Muler,140 Feitelson,141 Yokota and Tanimoto,142 and Steinberg and Katchalski,143 which are developed from Forster kinetics; and (b) those of Belikova and Galanin l44 and Voltz et al.,145-147 which are developed from diffusion theory and which extrapolate to Stern-Volmer kinetics. Yokota and Tanimoto,142 whose treatment is typical of group (a), used the Pade approximant method to evaluate an exact expression for dipoledipole transfer in a fluid solution in which the statistical distribution of IM* and Iy is determined by diffusion and by the decay and transfer of the IM* excitation. They obtained the following approximate expression for the 1M* fluorescence response function in the presence of [I Y), (11.109)

which becomes identical with the Forster relation (11.98) for B = 1. The parameter B is gi ven by B

=

(1 + 1O·87x + 15.5x2)3/4 1 + 8.743x

(11.110)

where

x = Drx- l !3 t 2!3

(11.111) (11.112)

578

Energy Migration and Transfer 11.10

An alternative approach has been developed by Voltz et al. 46 From diffusion theory (§9.1l) the rate parameter for a diffusion-controlled collision process is

kdiff = 47TN' DpR(1

+ pR(7T Dt)-1 /2)

(7.55a)

where R is the sum of the collision radii and p is the reaction probability per collision. Following Belikova and Galanin,144 Voltz applied (7.55a) to a diffusion-controlled dipole-dipole energy transfer process, by substituting R = R o, and p = 0·5, since Ro is defined as the critical distance at which the transfer probability is 0·5. The energy-transfer rate parameter thus obtained is

(kYM)t

=

27TN' DRo(1

+ 0·5R(7T Dt)-I!2)

The I M* fluorescence function is (11.114) where (11.115) (11.116) When

1/2 ", /k _ 2Ro[ly] t ~ 2A YM-(7TD)1/2 equation (11.131) reduces to iM(t) = iOM exp (-(kM + kyM[lYD t)

(11.117)

(11.92a)

which is the Stern-Volmer kinetic relation. Birks and Georghiou l34 have observed the donor fluorescence response function iM(t) of phenanthrene eM) in the absence and presence of [lY] (=0·5 [lY]o) of acridine in six solvents of viscosity TJ = 64·6 cP(cyclohexanol) to 0·4 cP (n-heptane). The results are shown in Figure 11.16. The data were compared with the relations of Forster (11.98), Yokota and Tanimoto (11.109) and Voltz (11.114). A mean value of Ro = 25·5 A is obtained from the spectroscopic data (11.89). At TJ = 64·6 cP, where V2DTM < R o, the IM* decay obeys Forster kinetics. At TJ < 3·7 cP, where V2DTM > 3R o, the I M* decay is exponential and obeys Stern-Volmer kinetics. At intermediate viscosities, where the decay is non-exponential but more rapid than predicted by the Forster relation (11.98), iM(t) agrees with the YokotaTanimoto relation (11.1 09), within the experimental error. Irrespective of the solvent viscosity, the Voltz relation (11.114) predicts a more rapid I M* decay than that which is observed. This is a consequence of the 'active sphere' approximation (R = R o, p = 0·5) which is used to describe the ,-6 dependence of the dipole-dipole transfer. Yokota and Tanimoto l42 do not

11.10 Influence of Diffusion on Energy Transfer

579

introduce any such approximation in describing the physics of the system. They obtain an exact expression for iM(t) and then evaluate this by a mathematical approximation to obtain (11.109). It appears likely that a more accurate evaluation of their exact expression by numerical analysis would yield an even closer fit with the experimental data. Elkana et al. 148 have studied the influence of diffusion on dipole-dipole transfer from naphthalene to anthranilic acid Y) in alcohols of

eM)

e

Time (ns)

Figure 11.16 Influence of solvent viscosity 'rJ on solutesolute energy transfer. Donor, phenanthrene eM); acceptor, acridine eY). Donor fluorescence decay curves. (a) pY] = 0; (b)-(f), pY] = 0·5 pY]o. (b), 'rJ = 64·6 cP; +, experimental data; solid curve, equation (11.98); (c)-(f), solid curves, experimental: (c) TJ = 27 cP; (d), 'rJ = 10 cP; (e), 'rJ = 3·7 cP; (f), 'rJ = 0·4 cP (after Birks and Georghiou 134) various 7], by observations ofjYM as a function of [Iy). In the most viscous solvent, glycerol (7] = 1000 cP), they found an unexpected discrepancy between the value of Ro = 27 A obtained from the energy transfer data, and that of Ro = 22·4 A obtained from the spectroscopic data and (11.89). t The jYM vs. [I Y) curves shift towards lower values of [I Y) with decrease in 7], which is qualitatively consistent with the expected increase in (RO)eff, but the uncertainty in the stationary Ro value makes quantitative comparison with theory less satisfactory. Birks and Leite l49 have made similar measurements of solute-solute transfer (AM against [lY)) in solvents of various 7]. In this case, the experimental and theoretical values of Ro agreed satisfactorily, and the relation between D and 7] was determined indepen-

t The difference between the experimental and theoretical values of Ro may be due to the neglect of higher multipole-multipole terms in the evaluation of the latter.

Energy Migration and Transfer 11.11

580

dently from studies of impurity quenching in the various solvents. Analysis of the data indicates satisfactory agreement with the theory of Yokota and Tanimoto.l42 It thus appears that in many systems radiationless singletsinglet energy transfer in fluid solutions is satisfactorily explained by dipole-dipole interaction, provided the effect of diffusion on the molecular distribution is taken into account. Other studies of singlet-singlet energy transfer have been reviewed by Terskoi et al. 209 11.11 Excitation migration and transfer in aromatic liquid solutions A binary liquid scintillator l consists of an aromatic solvent 1 M containing a mole fraction Cy (= [ly]/ P MD of a fluorescent solute 1 Y. 1M is usually benzene or one of its alkyl derivatives (toluene, p-xylene, etc.) and ly is a scintillator solute (§4.l1) of high qFY, short TFY, and adequate solubility. An ionizing particle which is stopped in the scintillator dissipates almost all its energy W in the excitation or ionization of the solvent molecules (the small fraction ~Cy dissipated directly in the solute molecules is negligible). The fraction of the dissipated energy W which results in TTelectronic excitation or ionization of 1 M is approximately I(TT), where I(TT) is the fraction of the electrons in 1M which are TT-electrons.l For benzene I(TT) = 12 ~ 0·14. The remaining fraction [1 - I (TT)] of W is expended in a-electronic excitation and ionization, and it is dissipated radiationlessly or results in transient or permanent radiation damage (radiolysis ). The primary ionization products, 2e- and 2M +, may combine with neutral molecules eM) to produce molecular anions, 2M-, and dimer cations, 2D +, respectively. The excited TT-electronic molecular species 1 M** and 3M** are produced by (I) direct excitation of 1 M by the primary particle, or by slow electrons (2e-), lM + W~lM ** 01.118s) lM+W~3M **

(11.118t)

(II) ion recombination, 2M+ + 2e-

~

lM* (or lM**)

(11.119s)

2M + + 2e-

~

3M* (or 3M**)

(11.119t)

The excimeric species lD** and 3D** are produced by (III) anion-cation recombination (§7.17), 2M+ + 2M-

lD**

(11.120s)

2M+ + 2M- ~ 3D**

(11.120t)

~

11.11 Excitation Migration and Transfer in Aromatic Liquid Solutions

581

(IV) dimer cation neutralization, (11.121s) (11.12lt) (V) association, IM* * + 1M ---+ ID**

(11.122s)

+ 1M ---+ 3D**

(11.122t)

JM**

The excited species IM **, 3M** and 3D** undergo internal conversion and dissociation yielding IM*, ID *, 3M* and 3D*. The dimer cations (2D+) of benzene, toluene, mesitylene and other aromatic hydrocarbons, which are important intermediates, have been observed as radiation products in low-temperature solutions. 15o Thomas 201 has recently determined the yields of excited species in liquid benzene irradiated by high-energy electrons using nanosecond pulse radiolysis and flash photolysis. The experimental values of G (yield per 100 eV of expended energy) are as follows: (a) (b) (c) (d)

G (singlet) from direct excitation, G~ = 0·4; G (triplet) from direct excitation, G~ = 0; G (singlet) from ion recombination, G~ = 1·2; G (triplet) from ion recombination, G~ = 1·7.

Gs refers to IM* and ID*, and GT refers to 3M* eD* dissociates). Gs = G~ + G~ = 1·6 agrees satisfactorily with the value of Gs = 1·55 ± 0·05 determined by Skarstad et a/.202 from a determination of the absolute scintillation efficiency of a solution of p-terphenyl in benzene. G~ originates from (11.118s), which yields IM** mainly in the S3 (lElu ) state, which associates (11.122s) and internally converts to IM* and ID* (§5.14). This process occurs with an overall quantum efficiency qMH = 0·45 (Table 5.9), so that the IM* * (lElu) yield by (11.118s) is G~=0·9. Since G~ = O, the yield of 3M** by (11.118t) is negligible. G~ originates from (11.119s), (11.120s) and (11.121s), yielding IM** and ID**, which internally convert to IM* and ID* with quantum efficiency q~H' G~ originates from (11.119t), (11.120t) and (11.12lt), yielding 3M** and 3D**, which internally convert to 3M* with quantum efficiency qIK' so that G~ qIK (G~)o (11.123) G~ (GDo

qt.m

where (Gi}o and (Gno refer to the yields of the primary processes. A value of (G~)o/(GDo = 3 is to be expected from multiplicity weighting, compared with the experimental value of G~/G~= 1·4. Brocklehurst203 has discussed

582

Energy Migration and Transfer 11.11

possible factors which might reduce (G~)o/(GDo below 3. An alternative possibility is that (qfK/qk.H) = 1·4/3 = 0·47. Ion recombination probably occurs into IM* and ID* (rather than into IM** and ID**), so that qk.H::: 1'0, and into the iso-energetic states 3M** and 3D**, which internally convert to 3M*. The estimated quantum yield of qfK ::: 0.47 for the latter process is similar to that of qMH = 0·45 observed for internal conversion within the singlet manifold (Table 5.9). Following the solvent excitation, IM* and ID* migration and diffusion leads to solvent-solute energy transfer IM*

+ Iy --7 1M + Iy*

(11.10) (11.10a)

and the resultant Iy* fluorescence corresponds to the prompt scintillation emission. 3M* diffusion and 3M* - 3M* interaction 3M* + 3M*

--7

IM*

3M* + 3M*

--7

ID*

+ 1M

(11.15) (11.16)

followed by solvent-solute transfer (11.10, 11.10a), leads to delayed Iy* fluorescence, which corresponds to the slow scintillation component (§11.8). The sequence of events by which the energy W of the ionizing particle is converted into Iy* fluorescence constitutes the scintillation process, and studies of this process up to 1963 have been described elsewhere. I The solvent-solute energy transfer process has been the subject of the most detailed investigations. Prior to the observation in 1962 of excimer fluorescence from the alkyl benzenes,151-152 the behaviour was described in terms of (11.10). The importance of the solvent excimers D*) is now recognized, although there are differing views on the role that they play in solvent excitation migration and transfer. Solvent-solute transfer can be studied by direct photoexcitation of the solvent in its first So - SI absorption band, thereby eliminating the preceding stages of the scintillation process. The solvent-solute transfer at normal temperatures obeys Stern-Volmer kinetics and can be described by an energy-transfer rate parameter k yM , or Stern-Volmer energy transfer coefficient GYM, given by

e

kyM[lM] GYM =

kM

(11.31)

The solvent-solute transfer quantum efficiency is (11.30)

11.11 Excitation Migration and Transfer in Aromatic Liquid Solutions

583

and the presence of Cy reduces the solvent fluorescence quantum yield and lifetime TM, respectively, to 10- 3 M), it should be noted that singlet-triplet as well as triplet-triplet interactions can lead to serious errors in the measurements of luminescence yields. 169 In some systems energy migration or transfer from higher excited states may be sufficiently rapid to compete effectively with internal conversion to a lower excited state. Liu and Kellogg l70 have observed energy transfer

Energy Migration and Transfer 11.13

594

from the second excited triplet state T2 of anthracene in mixed crystals of biphenyl or dibenzofuran (M) containing small concentrations of anthracene (Y) and naphthalene·d s (Z) at - 195°C. Anthracene was selectively excited (Esz > ESM > Ee. > Esy) and observations were made of the fluorescence yield tP Fy of anthracene and the phosphorescence yield tPpz of naphthalene. The low values of [lY] and [lZ], the low temperature, and the energies of the lowest triplet excited states (ETM > ETZ > E TY ) preclude the normal 3y* to 3Z* energy transfer processes (§11.7). However, the energy Eiy of the T 2 ey**) state of anthracene is such that Eiy > ETM > ETZ . The sensitized 3Z* phosphorescence is attributed to transfer to 1M, 3y** + 1M -r ly + 3M*

(1 1. 66b)

followed by 3M* exciton migration and transfer to IZ, 3M*+IZ -r IM+3Z*

(ll.1Ia)

The escape efficiency of the 3y** excitation is -10-4, and the anthracene T 2 lifetime is estimated as _10- 10 s. Such studies are of interest, since they provide a method of determining internal conversion rates and the lifetimes of higher excited states. 11.13 Intramolecular energy transfer When a molecule M (=X - A - Y) consists of two aromatic groups X and Y, separated by a saturated molecular structure A, such as an alkane chain, there is negligible conjugation between the 7T-electron systems of X, and they do not interact in the ground state. The 7T-electronic absorption spectrum ofM is practically equivalent to the sum of the absorption spectra of X and Y. For example, the absorption spectra of the I-naphthyl9-anthry I alkanes 171

g--3 ~ a~

.... ::I

=~

~

....,

0

("') 0

.g 0

= ::I

9.10,9.14

=-

'"

9.1,9.2,9.4 9.10 9.21 6.5 4.1,4.3 6.8 9.16,9.20 9.20 9.1,9.2,9.3,9.4,9.7,9.8,9.9,9.10 7.7 4.3, 11.5, 11.17 11.17 11.17 9.5, 11.3 11.5 0\

Ul Ie>

0'1 0'1

Table index of processes and parameters

Q

Process Electronic excitation

Flash photolysis

Absorption So - Sp

Sl-Sp So -Tq

Parameter Summary of photophysical processes Definition of rate parameters Assignment of electronic states Selection rules

Tables 2.1,2.2,2.3,2.4,9.22

Principal refs. §§2.2-2.4, 7.16, 9.9,11.1

Spin-orbit coupling Molecular structure

2.5,9.22 §§2.5,9.9 3.1,3.4,5.4,6.12,6.13,7.8,7.9 §§1.3, 1.4,6.6,6.11,7.14 §§1.4, 3.10, 3.11, 5.6, 5.12, 5.14 6.14 §§6.12, 6.13 1.1, 1.2, 1.3, 4.7 §1.2

Light sources Sl - Sp absorption Tl - Tq absorption

3.2 3.3,3.4 6.9,6.10, 6.11, 6.12, 6.13

§3.1O §3.10 §6.9

Spectrum Energy levels, Sp Extinction coefficient, € Oscillator strength, f Influence of environment 2-photon absorption cross-section n-photon absorption cross-section Spectrum Energy levels, Sp Spectrum Oxygen-induced spectrum Energy levels, T q

3.1,4.9, 5.8, 6.13, 6.18, 11.2 3.1,3.4,5.4,6.13 3.1,3.7 4.9 4.9, 5.8, 11.2 3.5,3.6,3.7 3.6 3.3 3.3, 3.4 6.3,6.12,6.13 6.8,6.12 6.3,6.8,6.12,6.13

§§3.1, 3.2, 3.9, 4.2, 4.12 §§3.9,5.1O §§3.3, 3.5, 3.6, 3.7 §3.7 §4.12 §3.11 §3.11 §3.1O §3.1O §6.8 §§6.8,1O.3 §§6.8, 6.10, 6.11

>-3

:.:>

5!: ~

SO Q., ~

~

0 ....,

.,0~ n

~

'"'" '":.:> ~

= :.:> ., :.:> Q.,

~

9 ..... ~

., '" ~

TI-Tq

Charge-transfer Excimer eD* - ID**)

Spectrum Extinction coefficient, Energy levels, T q Photoselection Spectrum, peak ECT Extinction coefficient, Spectrum

6.9,6.12,6.13 6.10,6.11 6.12,6.13 6.10 9.3, 9.4, 9.9 9.3

E'TT

E'CT

§6.9 §6.9 §§6.10, 6.11 §§6.9,6.12 §§9.2, 9.3, 9.4 §§9.2,9.4 §§3.10,7.16

~

e:: fI>

....

=-= fI>

~

a. ~

Q

n

fI>

Fluorescence SI -So

Spectrum, F(v) or Mo Influence of environment Quantum efficiency, qFM or yield,

§§4.3, 4.8, 4.9, 4.11 §§4.4, 5.4, 5.14, 6.13 §§5.4, 5.14, 6.13 §§5.4, 5.14, 6.13, 6.16 §§5.4, 5.14, 6.13, 6.16 §4.12 §§5.1, 5.13 §5.13 §5.13 §5.13 §§5.13, 6.14 §6.14

....~

0'1

Table index of processes and parameters (continued) Process Fluorescence QI-QO Excimer (lD*)

Tables

Parameter

Spectrum, etc. Spectrum, peak Dm Influence of solvent Lifetime, 'To = l/ko Quantum efficiency, qFO or yield,

7.4,7.6,7.7,9.17 9.17 7.3 7.3,7.7,8.1

~

Principal refs.

§6.14 §§7.1, 7.8, 7.9, 7.13, 7.16 §9.8 §§7.2-7.5, 7.8, 7.11 §§7.1, 7.2, 7.4, 7.8

r/JFO

Intramolecular excimers Mixed excimers DAcomplex Exciplex (lE*)

E-type delayed P-type delayed Recombination Electrochemiluminescence

Radiative lifetime, 'TFO = l /k Fo Internal quenching rate, kID Zero-point component of kID, kro Frequency-factor of kID, kio Activation energy of kID, WID Spectrum, etc. Composition Spectrum Lifetime Spectrum, peak Em Influence of solvent Quantum efficiency, qFE Lifetime, 'TE = l /kE Radiative lifetime, 'TFE = l /kFE Internal quenching rate, kJE Spectrum, etc. Rate processes Crystals Spectrum, etc. Spectrum, etc.

7.3 7.3 7.5 7.5 7.5 7.7 9.15 9.9,9.10 9.8 9.16,9.17,9.18,9.19 9.17,9.18,9.19 9.18 9.18 9.18 9.18 2.3 11.10

§§7.2, 7.3, §7.6 §§7.6, 7.8, §§7.6, 7.8, §§7.6, 7.8, §7.12 §9.7 §9.5 §9.5 §9.8 §9.8 §9.8 §9.8 §9.8 §§9.8,9.9 §§8.1-8.3 §§8.4--8.8 §1l.8 §8.1O §7.17

7.5, 7.8, 7.16 7.16 7.16 7.16

~

E: ~ ~ ~ ~

~

....'"tj 0

..,

0

n

~

'" ~

'" =

~

~

'"tj ~

....

~

-'" 51

~ ~

....

Phosphorescence

T 1 -S 0

Excimer (3D*) DAcomplex Recombination Dual

Spectrum, P(v)

6.3,6.5,6.12,6.13,7.10

Energy level, T 1 Lifetime, TT = l/kT

5.3,6.3,6.12,6.13,9.10 5.3,6.4,6.5,6.6,6.7,6.22, 7.11,9.12,9.13,9.14,9.27 12.1 6.2, 6.4, 6.6 6.2, 6.2A, 6.4, 6.6 6.2, 6.2A, 6.4, 6.6, 9.13 6.4,6.5,6.6,6.7 7.10 9.10 9.11,9.12,9.14 9.13

Quantum yield, CPPT Quantum efficiency, qPT Radiative lifetime TpT = l /kPT Heavy-atom effect Spectrum, peak Tm Spectrum Lifetime Internal quenching rate Spectrum, etc. Occurrence

~

§§5.5, 6.1, 6.4, 6.6, 6.8, 6.17, I)) 5!: II> 8.1,9.5 S' §§5.5, 5.10, 6.6, 6.10 §§5.5, 6.1, 6.4, 6.6, 6.7, 6.17, =~ 7.18, 8.4, 9.12 0 .... §§5.14, 6.1, 6.4 §§6.1, 6.5, 6.6 §§5.5, 6.1, 6.6, 6.12 §6.7 §§7.17,7.18 §9.5 §9.5 §9.5 §8.1O §5.13

...'0" n ~ til

~

I))

=-=

'a" ...

I)) I))

-... II> II> til

Internal conversion

SI - So Sp - SI SI - S0 (via isomer) Tq -Tl ID* _ ID O ID** _ID* Exciplex

Rate, kGM Quantum yield, CPGM Rate, kMH Quantum efficiency, qMH Influence of solvent Rate, kUM Quantum yield, CPUM Rate, kTK Rate, kGO Quantum yield, CPDJ Rate, etc.

5.5 6.1 5.7 5.9,5.10 5.9

5.10

§§5.1, 5.4, 5.11 §6.3 §§4.12, 5.1, 5.12- 5.14 §5.14 §5.14 §§5.14,6.16 §§5.14, 6.16 §§5.3, 6.14 §7.16 §5.14 §§9.8,1O.4

0'1

~

0\

Table index of processes and parameters (continued) Process

Parameter

lntersystem crossing Tl -So S1 -Tq

Rate, kGT Triplet quantum yield,

....

=

Q.

Quenching IM* (SI)

Self-quenching rate parameter, kOM External quenching rate parameter, kQM

3M* (T 1)

Quenching by O 2 Quenching by NO External heavy-atom effect Self-quenching rate parameter, kNT External quenching rate parameter,

6.19, 7.1, 7.3, J 1.15 9.20,9.21,9.23,9.24, 10.1 , 10.2,11.13 10.1,10.2 6.6,6.7 7.11 9.25,9.26,11.6

§§4.5, 6.16, 7.1-7.4, 7.7 §§4.5, 5.14, 6.7, 9.9- 9.11, 10.8,10.9 §§1O.4, 10.8, 10.9 §1O.6 §§6.7,6.13 §§7.18,9.12 §§9.12, 11.5

kQT

Quenching by O 2 Quenching by NO

§10.4 §10.6

tI> I> en ~

:::

Q.

'"':1

..,

~

~

-.., 5!n>

n> en

0\ 0\ -..I

Author Index (References to bibliographies are in italics)

Bagdasaryan, Kh. , 238, 298, 461 , 577, 622 Baker, R. F., 452 Bakhshiev, N. G., 116,140 Baldwin, B. A, 100-1 , 131, 139, 634, 640 Ban, M. I., 359, 392, 401 Bar, V., 623 Baranov, V., 298 Bard, A J., 371 Barnes, R. L., 131, 353, 359, 370, 573, 622 Basile, L. J., 370-1 Basu, S., 116,140,455 Batley, M., 452 Baur, E., 437, 490 Bayliss, N. S., 115, 140 Bazilevskaya, N. S., 132, 353, 359, 489 Bebb, R. B., 64, 83 Becker, R. S., 170, 191,464 Beckett, A, 183, 491 Bednar, T. W., 489 Beens, R., 417, 428, 490-1, 633, 640 Beer, M., 166,191 Belaev, L. M., 603 Belikova, G. S., 603 Belikova, T. P., 577-8, 623 Benesi, R. A, 411-13, 489 Bennett, R. G., 146, 181, 183, 191, 200, 253,297,575,591-3,622-3 Bensasson, R., 639 Benz, K. W., 603, 620 669

Abetino, F., 624 Abramson, E., 82,215,297,621 Abu-Zeid, M. E. M., 342, 345, 371 Adams, R. N ., 517 Adolph, J., 561, 565, 611, 621-2 Agranovitch, V. L. , 619 Aladekomo, J. B., 131, 353, 359, 403, 455,460,489,623,629,639 Albrecht, A. C. , 399,401-2,639 Aleksandrov, I. V., 199, 297 Algar, B. E., 132, 199, 201, 253, 297, 502-4,517,634-5,640 Allison, A. c., 412, 461, 489 Almy, G. M., 242,299 Amata, C. D. , 132, 137, 616, 624 Anderson, E. M., 241, 299, 628, 639 Andrews, L. J., 455, 467 Appleyard, J. R. , 370 Armstrong, A. T. , 170, 191, 359, 371 Arnold, G., 235, 298 Arnold, S. J. , 517 Astier, R., 223, 226, 278, 282-3, 298-9 Audo, W., 517 Avakian, P. , 82, 215, 297, 527, 560, 563, 565-6,610-11,619,621-2,624 Avery, E. c., 491, 621 Azumi, R., 371 Azumi, T., 183, 213, 226, 262, 297-8, 328,371,401 Babb, S., 110, 140 Backstrom, R . L. J., 538-9, 620 Badger, B., 623, 639

670 Berg, R . A., 82, 100- 2, 132, 139 Bergman, A., 298 Berlman, I. B. , 102-4, 106- 9, 122, 131- 2, 137, 139, 253, 359, 583, 623, 639 Bernstein, E . R ., 223 , 283, 297 Berry, M. G. , 401 Beukers, R., 461 Bhattacharya, R., 455 Bier, A ., 455, 467 Bilot, L. J. , 116, 140 Binsch, G ., 191 Birks, J. B., 37, 43, 62- 4, 82- 3, 86, 99-101, 103, 105, 131- 2, 137, 139, 168,171,175, 181,183, 191- 2,223, 253, 297,299,302,305,308,318,331, 334,353,359,361,363,370- 1, 373 , 376, 387- 8, 391, 393, 401 , 403, 408, 422, 425, 455,460,489,513,517,523, 573-4,578-9,584-9,613-14, 619-24, 639-40 Bixon, M ., 150, 191, 248, 299 Blackredge, 464 Blackwell, L. A., 262 Blount, E. R ., 623 Blum, H. F., 624 Boggus, J. D., 262, 470, 489 Bokozba, A., 278, 283, 299 Bolotnikova, T. N. , 140 Bonch-Bruevich, A. M., 603 Bonneau, R., 62,82 Boos, H ., 140, 191 Borisevich, N. A., 140 Bouas-Laurent, H., 640 Bouchard, J. , 442, 490 Boudart, M., 140 Bovey, F . A., 370 Bowen, E. J., 103-4, 119, 131, 140-1, 262, 439, 441 , 443-4, 446, 490, 508 , 510,51~529,577 , 619,622

Bowers, E. G., 253, 297 Bradley, L. T. , 64, 83 Braga, C. L., 191-2, 353, 359, 370, 614, 623 Bralsford, R ., 460 Brandon, R. W., 621 Branscomb, L. M. , 452 Braun, C. L., 171-2,191 Brewer, L., 132 Brewer, R. G. , 132 Briegleb, G ., 183, 262, 407-11, 415,

Author Index 452-3,455,461,467, 470, 489, 631 , 633,639-40 Brinen, J. S. , 183, 199, 222, 263, 278, 282,297 Brocklehurst, B. , 119, 141, 262, 398, 401- 2, 577, 581 , 622-4, 630, 639 Brodin, M., 619 Broude, V. L., 619 Brown, F. H ., 622 Brudz, V. G ., 624 Buck, W. L., 573-4, 622 BudD, A., 93, 139 Buettner, A. V., 83 Burch, D. S., 452 Burgos, J. , 298 Burland, D. M., 635, 640 Burr, J. G., 639 Burton, C. S., 245, 299 Burton, M ., 132, 137, 614 Buschow, K. H. J. , 298 Byers, G. W., 623 Cadas, J. P., 624 Cadogan, K. D ., 402 Calas, R., 321 , 370 Callis, J., 140 Calloway, A. R. , 181, 192, 288 Calvert, J. G., 599, 624 Calvin, M., 300, 461 Cameron, A. J. W., 363 Caris, J. C., 82, 621 Carter, J. G., 342, 345, 359, 371, 639 Castellan, A., 640 Castro, G. , 343-4, 371, 635, 640 Chakrabarti, S. K., 343-4, 371 Chandra, A. K. , 371 Chandross, E. A., 322,370-1,421,424, 430-1,489-90, 629 Chen, E ., 464 Chen, T. H ., 244, 299 Cheng Tsai, S., 633, 640 Cherkasov, A . S., 101 , 131-2, 139,353, 359,370,423,489-90 Cheung, H. T., 623 Chizhikova, Z. A., 79 Chock, D. P., 150, 192 Choi, S., 622 Chow, P., 639 Christodouleas, N. D., 297, 414, 419, 437,470, 489

Author Index Christophorou, L. G., 43, 99-100, 139, 216, 283, 297, 302, 342, 345, 359, 370-1, 404, 408, 422, 425, 464, 489, 629-30,639 Ciais, A., 119, 141 Claesson, S., 82 Clar, E., 3, 28, 54-8, 82, 183, 262 Clarke, R. H., 527, 619 Claxton, T., 619 Cobas, A., 622 Coburn, T., 82 Coche,A., 132, 137,297, 613-14,623 Cocivera, M., 631, 639 Cohen, N., 517 Cohen, S. G., 623 Colson, S. D., 223, 283, 297, 546, 621 Compton, R. N., 216, 283, 297, 404, 408,464,489 Conte, J. c., 171,191,370,613-14,623 Cooper, R., 82, 371 Corey, E. J., 517 Coulson, C. A., 2, 28 Courpron, C., 262, 624 Courtens, E., 238, 298 Cozzens, R. F., 598, 624 Crable, G. F., 460 Craig, D. P., 183, 219, 262, 278, 282,

297,525-6,619-20 Cross, G. L., 236, 298 Cundall, R. B., 242-3, 299, 630, 639 Curme, H., 140 Curran, R. K., 452 Cvetanovic, R. J., 628, 639 Czarnecki, S., 389,401 Czekalla, J., 183,262,410, 415-16,453,

455,461,467,470,489 Daigre, G. W., 297 DaIle, J. P., 639 Dalton, J. C., 183 Danby, C. J., 460 David, c., 597, 624 Davies, A. S., 299 Davydov, A. S., 34, 67-8, 116, 524-8, 619 Dawson, W. R., 132, 181,253,278,282,

288,300 Debye, P., 370, 398, 401 de Groot, K., 298 de Groot, M. S., 183, 248, 300 de Groot, R. L., 225, 298

671

de Maine, P. A. D., 455, 467 Demarteau, W., 624 Dexter, D. L., 539, 569, 576, 620 Dhingra, R. C., 191 Dickinson, T., 359, 363 Dikun, P. P., 183, 262 Dillon, M. A., 614 Djibelian, M., 298 Dokimikhin, N. S., 262 Dolan, E., 401 Dolby, L. J., 596, 623 Doller, E., 181, 359, 361, 363 Dombi, J., 93, 139 Donnini, J. M., 624 Donovan, J. W., 243-4, 299 Dorfmann, L. M., 82 Dorr, F., 262 Douglas, A. E., 241, 299 Drent, E., 625, 627,639 Drickamer, H. G., 602 Dubois, J. T., 262, 371, 517, 585, 613-

614,620,623-4 Duncan, A. B. F., 243-4, 299 DunnicIiff, K., 299 Dyson, D. J., 43,86,100-1,131-2,137,

139,305,308,353,361,370 Easterly, C. E., 639 Edelman, G. M., 139 Edwards, J. 0., 398, 401 Ehrenson, S., 464 Eisenthal, K. B., 418, 489, 635, 640 Eisinger, J., 370, 490, 624, 639 Eland, J. H. D., 460 El-Bayoumi, M. A., 300, 639 Elder, E., 191, 262, 470, 489 Elkana, Y., 579, 623 El Kareh, T. B., 624 EI-Sayed, M. A., 183, 262, 298, 401,

418,460,489,621 Erlitz, M. D., 267, 300, 639 Ermolaev, V. L., 183, 209, 262, 297,

537-8,590-1,620,623-4 Ern, V., 565, 611, 619, 621 Evans, D. F., 211-12, 268, 283, 297,

299,412,489,495,517,634,640 Evleth, E., 64, 83 Ezumi, K., 489-90 Faidysh, A. N., 536-7, 603, 620 Farragher, A. L., 452

672

Faure, J., 82 Feitelson, J., 577, 622-3 Ferguson, J., 262, 322, 328,370-1,421, 424,430-1,489-90,629 Field, F. H., 460 Fielding, P. E., 323, 370, 490 Filipescu, N., 597, 624 Finger, G., 632,640 Fischgold, H., 490 Flammersfeld, A., 620 Fletcher, F. J., 299 Flippen, R. B., 622 Flurry, R. L., 28 Foerster, G. von, 183 Foote, C. S., 517 Foote, J. K. , 246, 299 Forster, Th., 132, 139, 181, 314-15, 328, 353,359,361,370-1,390,441-2,445, 490,568-78,585,591,622 Foster, R., 408, 455, 460, 489 Fox, D., 526, 619 Fox, R. B., 598, 624 Frank, J. M., 442, 490 Franklin, A. R ., 79,83 Franklin, J. L., 460 Friedel, R. A., 55, 82 Frohlich, D., 67-8, 79,83 Frosch, R. P., 150, 167,183,191,262, 267,568-9,621-2 Furst, M., 132, 137, 622 Galanin, M. D., 79, 139, 570, 577-8, 622-3 Gallus, G., 620 Gangere, J. G. , 370 Garforth, F. M., 299 Garlick, G . F. J., 401 Garwin, E., 82 Gary, L. P., 239, 298 Geacintov, N ., 370, 624 Geldof, P. A., 191 Georghiou, S., 132,371,578-9,622 Gerkin, R. E., 621 Geuskens, G., 624 Giachino, J., 298 Gibbons, W. A., 236, 298 Gierke, T. D., 639 Gillette, P. R. , 242, 299 Gilreath, J. , 79 Glass, B., 624 Glass, L. , 346, 371

Author Index Glier, R., 489 Godfrey, T. S., 223, 278, 283, 297 Gold, A., 64, 67, 83 Goldsborough, J. P., 79,82 Goldschmidt, C. R., 630, 639 Goldsmith, G. J., 111,140 Goode, D. H., 567, 624 Goodman, L., 298, 464 Goppert-Mayer, M., 64,83 Gordon, R. D., 620 Gouterman, M., 140, 150, 191 Greenberg, A., 132, 137 Greenleaf, J. R ., 105,131-2, 137, 139, 181,310,353,359,361,370,589,616, 624 Gresset, J., 359, 361 Groff, R. P., 624 Gropper, H., 262 Grzywacz, J., 376, 401 Gschwendter, K., 534, 620 Guccione, R., 83 Gueron, M., 370, 490 Guseva, L. N., 640 Gutmann, F ., 239, 298, 408, 489 Hadley, S. G., 200, 220-2, 278, 282, 297 Haeberlen, D., 611, 622 Haebig, J., 370 Haken, H., 528, 619 Hall,J. L.,62,67,79,82,610,622 Ham, J. S., 175, 192, 489 Ham, N. S., 371 Hameka, H. F., 28, 226, 298 Hamilton, T. D. S., 57, 82, 139, 183, 191,238,263,298,370 Haminger, G. A., 243, 299 Hammer, A., 624 Hammick, D. L., 455 Hammond, G. S., 132, 183, 200, 253, 297-9,623 Hanada, K., 263 Hanle, W., 533, 536, 620 Hansen, H., 620 Hanson, D. M., 223, 297, 527, 619 Hanus, J., 79, 83 Hardwick, R., 506,517 Harrigan, E. T., 635, 640 Harris, P. V., 460 Harter, D . A., 242, 299 Hasegawa, K., 79 Hatch, G. F., 248, 267, 300

Author Index Hatchard, Co Go, 132, 297, 353, 374-5,

381,385,401 Haugland, R oPo, 597-8, 623 Hayashi, Ho, 491 Hebb, Mo Ho, 332, 371 Heckmann, Po H o, 532, 620 Heckmann, Ro c., 263 Hedges, Ro Mo, 408- 9, 464, 489, 597, 623 Heicklen, Jo, 517 Heilbronner, E., 191 Hein, Do Eo, 451, 491 Heinzelmann, Wo, 637, 639 Heisel, Fo, 613-14, 623 Helfrich, Wo, 563, 610, 620, 622 Helman, Wo Po, 132, 137, 635, 640 Henck, Ro, 297 Henry, B. Ro, 278 Herkstroeter, Wo Go, 183 Hernandez, Jo Po, 64, 67,83 Herre, Wo, 183, 262, 470, 489, 639-40 Herzberg, Go, 371 Hildebrand, Jo Ho, 411-13, 489 Hillier, I. H o, 329, 345-6, 371, 587, 623 Hilpern, Jo Wo, 168,183,191,449-51, 491 Hirayama, Fo, 116-17, 140, 172, 192, 250,300, 307, 310, 324, 370-1, 424,

489,576,622,636,638,640 Hirota, No, 550, 557, 621, 635, 640 Hobbins, Poc., 526, 619 Hochstrasser, Ro Mo, 168,191,209,262,

297-8,343-4,371,425,489- 90,527, 547,619,621,640 Hodgson, Wo Go, 183, 263 Holzman, Po, 238, 298, 640 Horrocks, Ao Ro, 103, 131, 139, 233,

253,297-8,490 Hoyland, Jo Ro, 464 Hoytink, Go Jo, 143, 162, 171, 191-2, 225,298,340,359,371,464,496,517,

635,640 Hubert-Habart, Mo, 263 Hudson, Jo A., 597, 623 Huebner, R o H o, 43, 216, 283, 297, 464 Hundley, L., 82 Hunt, Go R o, 150,191 Hunter, To Fo, 262, 640 Hush, No So, 464

673 Hutchison, Co Ao, 298, 548, 550-1, 557, 621 Hutton, Eo, 140, 401 Ianuzzi, Mo , 83 Il'ina, A. Ao, 140, 263 Ingold, C. K., 240, 299 Inokuti, Mo, 576, 622 Iredale, To, 262 Irvine, Jo Wo , 363 Ishii, Yo, 363, 490 Ishikawa, Ho, 243, 299 Itoh, K., 236-7, 298 Ivanova, To Vo, 131, 353, 623 Iwata, So, 416-17, 419, 470, 489, 491 Jablonski, A., 372, 401, 442, 490 Jackson, Go, 491 Jaffe, H. Ho, 54, 82, 602 James, C. Go, 132 Jankow, Ro, 191 Jano, I., 628-9, 639 Jansen, Ho Go, 533, 536, 620 Jarnagin, R oc., 79,238,298,322,370,

490,621-2,640 Jennings, Do Ao, 79, 82, 622 Johnson, Po Mo, 629, 639 Johnson, Ro c., 622 Joneleit, Do, 630, 639 Jones, Jo, 181, 361 Jones, Po Fo, 181, 192, 288, 298, 363, 451,491,634 Jones, Wo Jo, 83, 621 Jortner, Jo, 150,191-2,248,298-9,329, 371, 452, 525-8, 587, 610-1, 619, 621-3,625,639 Joussot-Dubien, Jo, 61,82,237-8,240, 298,639 Joyce, To Ao, 131-2, 199,253,297,396,

401,543,621 Judeikis, H. So, 183, 442, 490, 506-8, 517 Kaitu, Yo, 140 Kajigaeshi, So, 263 Kalantar, A. Ho, 249, 300, 629, 639 Kallmann, Ho, 132, 137, 139, 622 Kallmann-Oster, Go, 440, 490 Kanda, Yo, 262-3, 620 Kasha,Mo,144-5,161-4,166,171,183,

191,209,213,262,278,297,372,401, 436,460,490,517, 619 Kasper, Ko, 370

674 Katchalski, E ., 577, 623 Kato, S., 171- 2,191 Katz, J. L., 622 Kautsky, H., 501 , 517 Kawada, A., 238, 298 Kawaoka, K, 371, 425, 490, 501, 517 Kawski, A. , 116, 140 Kayama, K ., 28 Kazzaz, A. A., 139, 318, 331 , 334,353, 361,363,370,533-4, 620 Kearns, D. R ., 217, 223, 263, 297, 300, 371,425,461,490,493, 501,503 , 517 Kearns, G. L. , 460 Kearvell, A., 192, 297, 300, 490 Keefer, R. M ., 455, 467 Keller, R . A., 200, 220-2, 235, 278, 282, 297-8, 596, 623 Kellogg, R. E., 132,183,200,253,278, 288,297-8,451,491, 591 - 3, 623 Kemper, H., 140 Kepler, R. G ., 62, 82, 563, 565, 611, 621- 2 Ketelaar, J. A. A., 455, 467 Khan, A. U. , 370, 501, 503,517 Khan-Magometova, Sh. D ., 620 Khizhnyakov, V. V., 119, 141 Kholmogorov, V. , 238, 298 Kienzle, W. F., 620 Kikuchi, C., 371 Kikuchi, K, 299 Kikuchi, S., 533, 620 Kilin, S. F., 613 Kilmer, N. G. , 262 King, T. A., 131-2, 139, 181, 353, 361, 370,562,566,610- 11,620- 2 Kinoshita, M., 226, 298 Kinoshita, N., 460, 621 Kissinger, P. T., 639 Kistiakowsky, G. B., 241, 299, 628, 639 Klein, J., 434, 440, 490, 613-14, 623 Klevens, H. B., 55, 62, 82, 371 Kliger, D. S. , 639 Klimova, L. A., 140,262 Klopffer, W., 639-40 Knibbe, H ., 426-7, 429-30, 490 Kohler, B., 298 Kohlmannsperger, J., 603 Koizumi, M ., 140 Konebeev, Iu. V., 619 Konijnenberg, E., 329,371 Konishi, M ., 298

Author Index

Kopecky, K R ., 517 Koren, J. G., 183,263 Korolkova, O. N., 624 Korotov, S. M ., 140 Korsunskii, Y. M. , 603 Kortum, G., 453 Kotani, M. , 28 Kotschak, 0., 620 Kovalev, B. P., 603 Koyanagi, M., 175, 192 Kravchenko, A. D., 603 Krenz, F. H., 573, 622 Krishna, V. G., 298 Kropp, J. L., 132, 181, 288, 300 Kuchela, K N., 132, 192, 523, 573-4, 619,622 Kucherov, I. Ia., 536-7, 620 Kudryashov, P. I., 131 Kuhn, H., 626, 639 Kurskii, Yu. A., 577, 622 Kusakawa, H., 461 Kusuhara, S., 506, 517 Kuzmin, M. G., 640 Labhart, H., 200-1, 253, 278, 282, 297, 627-8,631,637,639 Lacey, A. R., 620 Lalande, R., 321, 370 Lambooy, A. M. F ., 371 La Mer, V. K, 370 Lami, H., 137, 297, 359, 361, 613-14, 623 Lamola, A. A. , 132, 183, 200, 245, 247, 253,297, 299,539,595,620,623-4 Land, E. J., 282 Lang, L. , 55,82 Langelaar, J., 347-8, 359, 371,450, 491 Laor, U., 174, 192 La Paglia, S. R., 297 Laposa, J. D., 132, 183, 288 Lapouyade, R ., 640 Lashlov, G. I., 598, 624 Latt, S. A., 596, 623 Laustriat, G., 132, 137, 297, 359, 361, 613-14,623-4 Lavalette, D., 282, 300 Lavrov, V. A., 140 Lawson,c. W., 116-17, 140, 172-6,192 Lazzara, C. P., 402 Lee, E. K . C., 243, 299 Lee, J. K., 517

Author Index Lee, S. K. , 639 Leermakers, P. A., 623 Legler, R. , 116, 140 Leiber, C. 0., 314-15, 370 Leibowitz, M., 192 Leite, M. S. S. c., 447, 513, 517, 579, 623 Lemaire, J., 245, 299 Leonhardt, R ., 426, 433, 437- 8, 489- 90 LescIa ux, R ., 237- 8, 240, 298 Levine, M ., 565, 611 , 621 Levshin, W. L., 401 Levy, L., 595, 623 Lewis, G. N. , 183, 372, 401 , 403 Lim, E. c., 132, 183, 288, 343-4, 371, 398,402 Limareva, L. A., 132, 353, 359 Linqvist, L., 82 Linschitz, R. , 398,401 , 448 , 491 Linschitz, L., 82 Lipkin, D. , 372, 401 Lippert, R. , 116,139,140, 164, 191 Lipsett, F. R., 98, 139, 529, 566-7, 620, 622 Lipsky, S., 116-17,140,171- 2,191-2, 246,299, 307,310,370,589,624, 636, 638,640 Liu, R. S. N., 593, 623 Livingston, R., 491 Lochet, R., 262, 624 Longuet-Riggins, R. c., 166, 191 Longworth, J. W., 371, 432-3, 491 Lovelock, J. E., 464 Lowdin, P.O. , 28 Lower, S. K. , 298, 409, 489 LUder, W., 140, 191 Ludwig, P. K., 132, 137, 616, 624 Lumb, M. D. , 131-2,177,181,191-2, 353, 359,361,370,614, 623-4 Lumry, R. , 370, 489 Lynch, F. J. , 137 Lyons, L. E., 239, 298, 408 , 452, 464, 489, 620 Ma, R., 624 Magel, T. T., 372,401 Mager, K. J. , 489 Mahan, G. , 526-7, 619 Mahr, R., 67-8, 79, 83 Maier, G ., 566, 611, 622 Majer, R. J. , 460 23

675 Makkes, van der Deijl, G., 639 Maksimov, M. Z., 622 Malliaris, A. J., 371 Mallon, M . R. , 299 Mallory, F. B., 299 Marchetti, A. P. , 217, 263, 297-8 Maria, R . J ., 639 Marisova, S., 619 Martin, T. E. , 249, 300, 629, 639 Mason, R. , 624 Mataga, N., 115, 131, 140, 298, 430. 489- 90,629,639-40 Matheson, M. S., 82 Mathews, C. W., 241, 299 Matsen, F. A. , 408- 9, 464, 489 Matsui, A., 363, 490 Matsui, R., 640 Matsumoto, R ., 640 McAlpine, R. D ., 168,191,640 McCartin, P. J ., 146, 181,191,253 McClain, W. M., 401 McClintock, R. M ., 79,82, 622 McClure, D. S. , 166, 183, 191, 209, 219-20, 226, 244, 262, 278, 297-9, 525, 619 McConnell, R., 408, 489 McCorkle, D . L., 639 McCoy, E. F. , 150, 191, 555-6, 621 McElroy, W. D., 624 McGlynn, S. P., 183, 191,210,213,226, 253, 262,297-8,328,359,371,387-8, 393 , 401, 414, 419, 437, 470, 489, 552- 6,621,639 McKeown, E., 517 McMahon, D. R. , 68, 79,83 McRea, E. G., 115,140,370 Medinger, T., 131, 210, 253, 297, 371, 401 , 490 Melhuish, W. R., 93, 98, 131, 139, 278, 444,491 , 613 Merrifield, R. E ., 560, 563, 565 , 610-11, 619,621- 2,624 Metcalf, W. S., 131, 443-4, 446, 490- 1, 508,510,517 Meyer, J., 262 Meyer, W. c., 401 Meyer, Y. R ., 226, 278, 282-3, 298-9 Mikhailov, B. M., 139 Mikhellashvii , M. S., 613 Mikiewicz, E. , 619 Miller, T . A. , 510, 517

676 Milne, D. G. , 299 Minchenkova, L. E., 139 Mirumyants, S. 0 ., 140 Misra, T. N., 527, 555-6, 619, 621 Mokeeva, G. A., 353, 623 Molchanov, V. A., 131, 139 Moll, F ., 140 Moodie, M. M ., 262, 415, 489 Moore, G. F., 183, 191, 263, 401, 640 Mori, Y., 628, 639 Morikawa, A., 628, 639 Morris, R., 298 Morrison, J. D., 460 Mottl, J., 460 Moulines, F., 370 Muel, B., 263, 389,401 Mulac, W. A., 299 Muler, A. L. , 577, 622 Milller, H. P., 621 Mulliken, R. S., 82, 404, 410-13, 439, 453,489,493- 6,517 Munck, A. u., 517 Munro, I. H., 43, 103, 132, 139, 168, 183,191,263,278,305,308,353,359, 361,370,401,620,622,640 Muromtsev, V. , 298, 461 Murray, R. W., 298 Murrell, J. N., 28, 327, 371, 413- 14, 439,489,494, 496,517 Nafisi-Movaghar, J. , 614, 623 Nagakura, S., 417, 470, 489, 491 Nagele, W., 139, 140 Nakashima, T. T., 363 Nakato, Y., 83 Nakayama, T., 460 Nakomoto, K, 409, 489 Naqvi, K R., 390, 394,401,614,623 Nasielski, J., 105,132, 139 Natusch, D. R . S., 131 Nauman, R. V., 169,191,263 Navon, G. , 639 Neporent, B. S., 110, 116,140 Ness, S., 137 Neznaiko, N. F ., 423, 489 Nicholson, A. J. c., 460 Nicol, M ., 363 Nieman, G. c., 249,262,267,283, 300, 544-5,547,620- 1,639 Nikitina, A. N ., 139 Nishimura, H., 131, 353

Author Index Nishizaki , S., 461 Nordin, S., 541,621 Norrish, R. G. W. , 60, 82 Northrop, D. c., 363,531,603,620 Novak, J. R ., 61, 82-3, 278, 282 Novros, J. S., 446, 491 Noyes, R. M., 370, 446, 491 Noyes, W. A., 240, 242-3, 245, 299 Nurmukhametov, P. N., 262 Obyknovennaya, I. E., 359, 423, 489- 90 O'Dwyer, M. F., 235, 300, 639 Offen, H . W., 363, 451, 491, 639 Ogryzlo, E. A., 517 Ohno, K, 28 Okada, T., 489-90, 640 Olness, D ., 183, 298 Onsager, L., 113, 140 Oohari , H., 490, 640 Ooshika, W ., 115, 140 Oppenheimer, M., 619 Orchin, M., 54--5, 82, 602 Orgel, L. E. , 413, 489 Ory, H. A., 191, 263 Osborne, A. D., 511,517 Oster, G., 370 Ota, Y., 639 Pack, J. L., 452 Padye, M. R. , 183, 262 Page, F. M., 452 Page, S. G., 131 Pantell, R ., 64, 67,83 Pao, Y. H., 64,83 Parker, C. A., 100, 131- 2, 139, 199, 204--5,253, 297,353,371, 373-5, 381, 385, 389- 91, 396, 398, 401, 542-3, 591 , 621,623 Pariser, R., 10,28,67,83,224--7,297 Parmenter, C. S., 247, 299, 628, 634, 639-40 Parsons, B. N. , 455 Pavlopoulos, T. , 298 Pekkarinen, L., 448, 491 Peone, J., 467 Pereira, L. c., 192 Perkampus, H. H., 363 Perkins, W. G., 566, 611, 622 Perrin, F. , 441, 490 Person, W. B., 452

677

Author Index Pesteil, L., 119, 141,262-3 Pesteil, P., 119,141,263 Peterson, O. G., 83 Peticolas, W. L. , 62-3, 79,82-3 Petrov, A. A., 183 Petruska, J., 57, 192 Pfeffer, G. , 137, 297 Phelps, A . Y., 452 Phillips, D. H., 245, 299, 629, 639 Phillips, D. T., 639 Phillips, H. B., 622 Pitts, J. N., 299, 599, 624 Platt, J. R ., 4-8, 10,28, 55, 57, 62, 82, 224,371,489 Pohl, L., 363 Polacco, E., 83 Poole, H . G., 299 Poole, J. A ., 191, 299 Pope, ~.,238,298,624 Pope, R., 370 Pop Ie, J. A., 28, 464 Popova, E. G., 262 Port, H., 557-9, 620 Porter, G., 60-1, 82, 183, 219, 223, 225-6,253,278,282-3,297,401,448, 450, 491,506,511,517, 540,621 Pradere, F., 64, 79, 83 Prater, B., 517 Price, W. C., 460 Prigge, H., 140 Prikhot'vo, A. F., 619 Pringsheim, P., 490 Proch, A., 239, 298 Prochurow, J., 640 Propstl, A., 620 Pukhov, R. K., 199,297 Pullman, A., 624 Pullman, B., 28, 624 Puthoff, H., 83 Pysh, E. S., 461 Rabalais, J . W., 639 Rabaud, ~., 262 Radzievskii, G. B., 620 Ramsay, 1. A., 278 Rashba, E. I., 619 Rau, J. D., 634, 640 Raviart, A., 613 Ray,J. P., 183, 191,238,263, 298 Rebane, K. K., 119,141 Rees, W. T ., 131, 139

Rehm, D ., 490 Reich, H. J. , 517 Reid, C., 262, 415, 453, 489 Reilley, C. N., 639 Reinhardt, P. W., 216, 283, 297 Remko, J. R., 491 Rentzepis, P. ~., 64, 69,83,142,166-7, 191-2,625-7,639 Rettschnick, R . P. H. , 191,371 Reynolds,~. J., 297 Rhodes, W. , 183,262 Rice, S. A., 192, 329, 346, 370-1, 525-8, 587,619,622-3,629,639 Richardson, P., 622 Richter, H. P. , 490 Ridley, R . G., 460 Rieckhoff, K. E., 63, 79, 82-3 Riehl, N., 139 Robertson, W., 110,140 Robinson, G. W ., 150, 167, 183, 191, 223, 240-1, 243, 248, 262, 267, 283, 297- 9,527,544-7,568,619-22,626, 633,635,639-40 Rodemeyer, S. A., 132, 137 Rohatgi, K. K., 439, 490 Rollefson, G., 140 Rollig, K., 429, 490 Rosen, P., 139 Rosenblatt, G. ~., 132 Ross, 1. G., 150, 183, 191, 219, 262, 278, 282,297 Rousset, A., 262, 547, 624 Rousset, Y., 557, 624 Rozman, 1. ~., 613, 622 Ruedenberg, K., 371 Russell, R. D., 639 Ruzevich, Z. S., 166, 191 Sahu, J., 103-4,131,441,490 Samson, A. ~., 577, 622 Sander, W., 620 Sandros, K., 538-9, 620 Sangster, R. c., 363 Sarkanen, K., 82 Sarti-Fantoni,619 Sato, S., 243, 299 Schafer, F. P., 429, 490 Scharmann, A., 620 Schenck, G. 0., 503, 517 Schlag, E. W., 243, 299 Schmidt, D., 191

678 Schmillen, A. , 11 6, 140, 489,603, 619, 639 Schnaithmann, R ., 620 Schneider, W. G. , 83, 563, 610-11, 621-2 Schnepp, 0 ., 526, 595, 619,623 Schoental, R. , 139 Schott, M., 79, 83 Schug, J. c., 629, 639 Schi.iler, H., 235 , 298 Schuster, H ., 639 Schuyler, M. W. , 247, 299 Schweig, A. , 626, 639 Schweitzer, D., 401 Schwenker, R. P., 183, 451 , 491,623 Scott, D. R. , 170, 191, 464 Scott, E . J. y. , 139 Scott, J. R. , 517 Seibold, I., 140 Seibold-Blankenstein, I. , 139 Seidel, H. P., 132, 181, 314--15, 353, 359, 361,370 Seifert, H. G. , 63-4, 83, 610, 622 Selinger, B., 131- 2, 181,353, 359, 361, 370,490 Selivaneko, A. S., 577, 622 Seybold, P. G ., 102, 140 Shepherd, P. J. , 460 Sheremet, M., 620 Sherman, P . D ., 299 Shimada, R. , 262-3 Shindo, K., 245, 299 Shipley, E. D. , 131 Shirokov, V. I., 132, 353, 359 Short, G . D., 371 Shpak, M. T ., 620 Shpol'skii, E . V. , 118-19,140, 262-3 Shulman, R. G. , 370, 490 Sidman, J. W. , 166, 191 , 262,620 Siebrand, W., 83, 147- 50,152-61 , 167, 183, 191, 245, 451 , 491 , 501 , 567, 621- 2,634, 640 Siegel, S., 183, 298, 442, 451 , 490- 1, 506-8, 517, 634 Siegoczynski, R ., 640 Sigal, P. , 243, 299 Silbey, R ., 527, 619 Silver, M., 79, 238, 298 Simpson, J. D. , 639 Simpson, 0. , 363, 531, 603, 620 Singh, S., 62-4, 82-3, 566-7,610,621-2

Author Index Sinitsyna, Z. A. , 298, 461 Skarstad, P., 581, 624 Slifkin, M . A., 328, 371, 408, 412, 455, 460- 1, 489 Sloan, G. J., 530, 620 Smaller, B., 449, 491 , 540, 621 Smith, F. J., 191, 359 Smith, F . W. , 619 Smith, G . C., 563, 622 Smith, S. J., 452 Smith-Saville, R. J ., 137 Smolisky, G. , 298 Smoluchowski, M. von , 31 2,445- 6, 491 Snavely, B. B., 83 Song, P. S., 627, 639 Soref, R . A. , 79, 83 Spangler, J. D., 262 Sponer, H. , 183, 262, 620 Srinivasan, B. N ., 253, 387-8, 393 , 401 , 621 Stacy, W. T., 564, 624 Staiger, W ., 139 Stafford, F . E. , 132 Steinberg, I . Z., 577, 623 Steingra ber, O. J. , 132, 137, 139 Stephenson, L. M., 298 Stern, 0 ., 36, 441 , 490 Sternlicht, H. , 559, 621 Stevens, B., 111,131-2, 140,181,183, 199,201,253,297, 301 , 318,359,361, 363, 370, 391-2, 401 , 502-4, 517, 631, 634--5,639-40 Stevenson, P . E., 57 Stief, L. J., 183, 450,491 Stobl, G. , 528, 619 Stockburger, M., 140 Stoicheff, B. P ., 62,82- 3, 621 Stolzle, K., 621 Strickler, S. J., 82, 100- 2, 132, 139, 300, 639 Strong, R. L., 541 , 621 Stryer, L. , 82, 597-8, 623 Sukulov, u., 452 Sullivan, P. J. , 236, 298 Sullivan, S., 298 Sun, M. , 627, 639 Suna, A. , 611, 619 Sveshnikov, B. Ya. , 131, 183, 262,353, 623 Sveshnikova, E. B., 590-1 , 623 Svishchev, G. M ., 119, 140

Author Index Svitashev, K. K., 209, 262, 297 Swank, R. K., 573-4, 622 Swenberg, C. E., 564,624 Swenson, G. W., 402 Swicord, M., 298 Switendick, A. C. , 565,611,622 Szent-Gyorgi, A., 461, 624 Szollosy, L., 93, 139 Szoke, A., 611, 621 Takahashi , K., 490 Tanaka, c., 401 Tanaka, J., 327, 371, 401, 417, 470, 489 Tanaka, M., 299 Tanaka, Y., 460 Tanelian, C., 613- 14, 623 Tanimoto, 0., 577- 80, 623 Tate, J. T., 452 Tavares, M. A. F. , 490 Taylor, J. A., 262 Taylor, W. c., 517 Teale, F. J. W., 131, 624 Teplyakov, P. A., 183, 262 Terenin, A. N., 298, 537, 620 Ter-Sarkisian, G. S., 139 Terskoi, Ya. A., 576, 580, 624 Thirunamachandran, T., 619 Thoma, P., 621 Thomas, J. K., 82, 371,581,624 Thomaz, M. F., 131-2, 181,361 Thompson, C. E., 267 Tickle, K., 297, 490 Tomkiewicz, Y., 639 Tomura, H., 131,353 Topp, M. R., 61, 82 Torihashi, Y., 639 Trencseni, J., 640 Trlifaj, M. , 528, 619 Trozzolo, A. M., 236, 298 Trusov, V. V., 183, 262 Tsubomura, R., 83, 493-6, 517 Tsukada, K., 533, 620 Umberger, J. Q., 370 Unger, I., 240, 299 Vahlensieck, H. J. , 183, 262, 470, 489 Vala, M. T., 329,370- 1,587,619,623, 629 Vander Donckt, E., 105,132,139 van der Waals, J. R., 183, 248, 300

679

Van Remert, R. L., 517 Van Kranendock, J., 83 vanLobenSels,J. W.,371, 585, 613-14, 623-4 Vaubel, G., 621 Vavilov, S. , 143-4, 161-2, 172, 177, 377-8,441-2,490 Veljkovic, S., 140 Vember, T. M., 131, 139, 370 Vesley, G. F., 298 Vilesov, F. 1.,460 Vinokurov, L. A., 401 Visco, R. E., 371 Visnawath, G., 166, 191 Vogel, F ., 624 Voldaikina, K . G., 131, 139 Volmer, M., 36,441,490 Voltz, R., 562, 566, 577-8, 584-9, 613-14,616,621,623 Voss, A. J. R., 299, 630, 639 Voss, W., 139 Wacks, W. E., 461 Walker, G ., 168, 171,191,623 Walker, M. S., 183, 401, 431-3, 489 Walmsley, S. R., 525- 6, 619 Walsh, J. R., 526, 619 Walz, R., 453 Ward, R. R., 299 Ware, W. R., 100-1 , 131-2, 139, 236, 298, 446, 490-1 , 508-13, 517, 613, 626,635,639 Wasserman, E., 298 Watanabe, K., 460 Waters, W. A., 517 Watts, R . J., 639 Wauk, M. T., 298, 621 Weber, G., 131, 624 Webman; I., 625, 639 Weinreb, A., 174, 192, 588, 622-3 Weiss, J., 437, 490 Weisz, S. Z., 79,621-2 Weller, A., 314-15, 370, 417, 425-7, 429, 433, 437-8, 445, 489-91, 624, 633,640 Wen, W. Y., 402 Wentworth, W. E., 464 Wexler, S., 517 Weyl, D. A., 131, 353, 359 Wharton, J. R., 191, 263 Wheeler, R. C., 452

Author Index

680 White, A. H., 299, 628, 639 White, J. W., 620 Whitten, D . G., 298 Wiederhorn, S., 602 Wiggins, P. M., 131 Wiliarat, P. , 131 Wilkinson, F., 131, 192, 210, 233, 253, 262, 297-8, 300, 371, 401, 436, 448, 490,540,620-1 Williams, A. H., 131 Williams, D. F., 157-61, 183, 191, 561, 565,611, 621-2 Williams, F. E., 332, 371 Williams, R., 111, 140 Wilson, T. , 517 Windsor, M. W., 61,82-3,219,225-6, 278,282,297,506,517 Wirth, H. 0., 132, 139, 140 Wishnok, J. S., 299 Witzke, H., 517 Wolf, H . c., 525, 529-30, 534- 5, 557-9, 603,619- 20, 622,624 Worlock, J. M., 83 Wright, F. J., 278

Wright, G. T., 529, 619 Wright, M. R ., 262, 448, 491, 621 Wyeth, N. c., 491 Yager, W. A., 298 Yamamoto, N ., 83, 490 Yamane, T., 370, 490 Yanari, S., 370 Yang, M. Y., 402 Yang, N. c., 461 Yates, J. M., 401 Yatsiv, S., 526,619 Yguerabide, J., 616, 624 Yildiz, A., 639 Yokota, M., 577- 80, 623 Yoshimura, S. , 79 Zachariasse, K., 433, 491 Zahlan, A. B., 79, 533-4, 620-1, 632, 640 Zander, M.,183,262-3, 374,402 Zandstra, P. J., 639 Zima, V. L., 536, 603, 620 Zmerli, A., 262

Subject Index Main text references are in bold type and references to tables in italics. References in italics in parentheses refer to Table index of compounds (pp. 641- 59) or Table index of processes and parameters (pp. 660-7) a-bands, 54, 56-8, 105,525-6 a-phosphorescence (see Delayed fluorescence, E-type) Absorption, 30-4, 44-83 biphotonic (see Absorption, multiphotonic) charge-transfer (see Charge-transfer absorption) Clar classification of bands, 54-8 cross-section, 47, 49, 64, 79-80, (660) crystal, 523-8, 601-2, (666- 7) environmental effects, 109-19, 138, 165,188,527-8,626 (660) excimer (see Excimer absorption) Ham band, 175 hot bands, 45-6, 223, 540 molecular ion, 437-8 muitiphotonic, 32-4, 38, 62-9, 79-81, 561, 625, (660) NO-induced, 212, 242,283,493,496, 625, (666) oxygen-induced, 211-12, 223, 242, 268, 283, 412, 492, 494-6, (660, 666) Platt (PFEO) classification, 4-10, 54-6, 62, 70-5, 78, 208, 224-8, (660) self (see Self absorption) Qo - Qb 237 So - Sp, 8-10, 30-3,38,44-58,60,62, 70-5, 86-8, 105, 138, 172, 217, 561,627, (660) 681

Absorption-continued So - T q , 8, 30-3, 38, 63, 208, 211-18, 222-6,242,256-9,268,283,412, 492-3,494-6, 527,(660) SI - Sp, 10, 30-3, 38, 58-62, 77-8, 225, 625, (660) To - Tb 236 TI - T q , 10,30-3,38,40,59, 196-7, 199-200, 218-26, 236, 269-84, 591, 625, 628, 635, (661) Acenaphthene (2Z), 22, 123, 127, 178, 251,258,356, 385,459,466, 533, (644) Acenaphthene· d io (2Zd), 22, 258, (644) Acenes,3, 7-10,56,62,118,224-8,338, 529 (see also Individual compounds) 3-Acetophenanthrene, 259, (647) 9-Acetophenanthrene, 259, (647) Acetophenone, 268, 605, (653) 9-Acetoxyanthracene (3.1K), 23, 121, 321,352,356,475, (646) Acetylene, 3 Acridine, 120, 123, 268, 281, 434, 476, 481,575,578-9,603, (653) Acridone, 120, (653) Acriflavin, 207, 254, 399, (653) 'Active sphere' model, 441-7, 506-8, 538,546,572-3,576,578 Pldenine,424-5,600 AD exciplex (see Exciplex, acceptordonor)

Subject Index

682 Alkaloids, 600 Alkyl bromide, 482, (653) Alkyl chloride, 482, (654) Alkyl cyanide, 482, (654) Alkyl iodide, 482, (654) 9-Arninoacridine, 120, (654) l-Arninoanthracene, 123, (646) 2-Arninoanthracene, 123, (646) 9-Aminoanthracene, 121, (646) 3-Aminofluoranthene, 123, (652) 3-Arninophthalimide, 626 4-Arninophthalimide, 626 5-Amyll: 2-benzanthracene (4.3T), 24, 358, (649) Anharmonicity, 155-8, 249-50 Aniline, 122, 408, 421, 425, 437, 484, (654) Anion-cation association, 40, 340-2, 433,580-1 Anisole, 122, (654) Anthanthrene (6.1),14,74,133, 184- 5, 199, 201, 252, 358, 363, 460, 603, (650) Anthanthrene'd 12 (6.1d), 185, (650) Anthracene (3.1),11,22, (645) absorption, 55-6, 62-4, 67-8, 70, 79-81, 86, 92, 118, 213, 220, 224-6,268,271,280,284,526-8, 560-1,601-2,625 crystal, 62-4, 67-8, 79-81, 170, 224, 316-19, 323, 339, 362, 524-37, 559-67, 586, 593, 601-4, 610, 625 Davydov splitting, 67-8, 170, 524-7, 601 delayed fluorescence, 62-3, 316,385, 39f-7, 433, 542-4, 556-7, 559567,632 diffusion, 510, 515-16 dimer, 316-17,319-23,338,424,493, 629, 633 donor-acceptor complex, 415, 454, 466,468-71 electronic states, 5-9, 67-8, 70, 184, 224-6,232-3,284,290,459,462, 526-8 energy (or exciton) transfer, 319, 341, 396-7, 528-37, 594, 603, 606, 613 excimer, 170,316,319,330,339,341, 347-8,362,36~369,450,629

Anthracence-continued exciplex, 423-4, 427-9, 438-9, 475-6, 478 fluorescence, 62, 86, 92, 97, 107, 111, 118, 120-1, 123, 127, 133, 170, 178,224,231,251,286,341,362, 433, 438-41, 485, 508, 529-39, 564 impurity quenching, 198-9, 439-46, 449-50,485-6,500,506,508-15, 530,613,635 peroxidation, 492-3 phosphorescence, 182, 258, 284, 347-8,470,562-3 radiationless transitions, 178, 182, 185, 201, 224, 230-3, 251, 286, 289,561 singlet exciton migration, 319, 528537,586,604 triplet exciton migration, 559-67, 610 triplet lifetime, 182, 347-8, 369, 449451,471,486,488 triplet-triplet interaction, 62-3, 239, 559-67 Anthracene'd IO (3.1d), 22, 123, 127, 129, 179, 182, 185, 230, 251, 280, 286, 289,451,488, (645) 9-Anthracene carboxylic acid (3.1L), 23,121,321,352,356,(646) Anthranilic acid, 579, 603, (654) Anthranol, 341 Anthraquinone, 603, 605, (654) Anthrone, 597, 635 9-Anthroyl acetone, 495 Argon ion laser, 69 Aspirin, 600 l-Azaanthracene, 268, (647) 2-Azaanthracene, 268, (647) l-Azapyrene, 268, (654) Azulene (G), 26, 31, 69, 75, 123, 131, 143,161-2,166-8,171 , 179,184-5, 187,236,460,464,511,527,625-8, (653) Azulene ' d 8 (Gd), 26, 185, 187, (653) l-Azuloic acid, 166 Band model (see Exciton band model) Bathochromic shift, 56, 107 BBD, 134, 137, (653, 655) BBO, 134, 136, (653, 655) BBOT, 124, 135, 137, (653, 655)

Subject Index Beer-Lambert law, 58 Benesi-Hildebrand relation, 410-3 Benzaldehyde, 605, (654) 1 :2-Benzanthracene (4.3), 4, 11, 24, 466,633, (648) absorption, 58, 71, 77-8,81,273-4, 280,454,459,469 crystal, 362, 547 delayed fluorescence, 385, 388, 632 electronic states, 71, 78, 179, 184, 459,463 excimer, 314-16, 330, 349, 352, 357, 362,367,475,627,631-2 fluorescence, 81,129,133,179,252, 314-16, 352, 357, 362, 468-9, 476,547,637 phosphorescence, 182, 259, 416, 470-1,488,547,606,637 radiationless transitions, 179, 182, 185,187,201,252,287,289,627 1: 2-Benzanthracene· dl2 (4.3d), 24, 129,182,185,287,488,(648) Benzazulenes, 166 Benzene (1),1-4,11,20, (641) absorption, 46, 53-7, 62, 70, 77-8, 110,117,172,212,223,240-2, 268-9, 283, 291, 526, 591, 625, 635 crystal, 212, 223, 283, 525, 545-7, 586,635 Davydov splitting, 525-6, 635 deuteration, 20, 122, 126, 185, 211, 248-50,267,294-6 donor-acceptor complex, 408, 417, 453-4,465,470,494,496 electronic states, 2, 7, 9, 29, 62, 70, 78, 104, 178, 184, 216-18, 223-5, 231,283,457,462 energy migration, 580-90, 614-15 energy transfer, 570, 583-90, 605, 613 excimer, 62, 175,329-30,342,346-7, 351, 354, 367, 581, 587-8, 615, 629-31, 635-6 fluorescence, 90, 106-7, 110, 117, 122,126,133,171-7,178,240-8, 250,292,342,351,354,545-7, 616,628,635-6 internal conversion, 146, 161-2, 171-7, 185, 187, 189-90, 234, 245-8

683

Benzene-continued internal quenching, 146, 161, 178, 180,240-50,351 intersystem crossing, 176, 182,234-5, 286,289,293-6,451 isomerization, 146, 177, 234,245-8, 629 liquid, 62, 77-8, 171-7, 189, 342, 354, 580- 90,613-16,629,635-6 phosphorescence, 182, 208, 211, 256, 267,283,470,545-7,591,629 triplet lifetime, 177, 182, 211, 248-50, 267,295,451,629 vapour, 9, 110, 117, 175, 177, 189, 216-18, 240-8, 283, 291-3, 628-9 Benzene·d 6 (ld), 20, 122, 126, 178,182, 185,211-12,223,243,247-9,256, 267, 269, 292-4, 451, 457, 545-7, 628-9,635-6,(641) Benzidine, 124, (654) 1: 14-Benzobisanthrene (9.1), 18, 75, 184, (651) 1 :2-Benzochrysene (5.10),13,73,184, 260, 363, (650) 5: 6-Benzochrysene (5.11), 13, 73, 184, 260, 363, (650) 1: 2-Benzocoronene (8.4), 18, 130, 181, 186,253,255,277,281,287, (651) 1:12-Benzofluoranthene,169 2: 13-Benzofluoranthene, 261, (652) 3: 4-Benzofluoranthene, 261, (652) 1 :2-Benzofluorene, 169,261, (652) 2:3-Benzofluorene, 261, (652) 3:4-Benzofluorene, 169,261, (652) 4:5-Benzofluorene,169 Benzonitrile, 268, (654) 1: 2-Benzopentacene (6.6), 15, 74, 184, (650) 1 :2-BenzoperyJene (6.3), 14, 74, 184, 287, (650) . 1: 12-Benzoperylene (6.2),14,74,77-8, 130, 181, 184, 253, 260, 358, 363, 463,477, (650) 2: 3-Benzoperylene (6.4), 14, 74, 184, (650) 3: 4-Benzophenanthrene (4.5),4, 11,25, 71,104,182,184-5,187,259,275, 281,330,367,459,463,(649) 3 :4-Benzophenanthrene· dl2 (5.4d), 25, 185, (649)

Subject Index

684 Benzophenone (N), 27, 281, 537-8, 547-8, 595-7, 598, 605-6, 635, (653) 1 : 2-Benzopyrene (5.2), 12, 72, 182,

184-5,187,260,358,455,460,463, 477, (649) 1: 2-Benzopyrene ' dl2 (5.2d), 185, (649) 3 :4-Benzopyrene (5.3), 12, 62,72,77-8,

81,118,130, 144,162, 171,184-5, 187, 238, 260, 268, 275, 289, 319, 341 , 358, 362, 385-6,389,455,460, 463, 477, 600, (649) 3:4-Benzopyrene ' d I2 (5.3d), 185, (650) 5: 6-Benzoquinoline, 268, (654) 7 : 8-Benzoquinoline, 268, (654) Benzoquinolyl, 452, (654) p-Benzoquinone, 408, 452, (654) 1: 2-Benzotetracene (5.5), 12, 72, 184,

(650) 1 :2-Benzotetraphene (5.12), 13, 73,

184, (650) 3 :4-Benzotetraphene (5.13), 13, 73,

133,184,477,(650) Benzoyl chloride, 268, (654) Benzvalene, 629 Benzyl acetate, 122, (654) Benzyl alcohol, 122, (654) 4-Benzyl biphenyl, 123, (652) 9-Benzylone anthracene, 321 ~-bands,54,56-8, 143,525-6,529 ~-phosphorescence (see phosphorescence) Biacetyl, 242, 281, 511, 513, 538-40,

584-5,605-6,613, (654) 3,3' -Bifluoranthyl, 123, (652) Bimolecular processes, 34-7, 40- 1 (see also Energy migration, Energy transfer, Quenching) heteropolar, 34-6, 41, 433 homopolar, 34-6, 40, 564 rate parameters, 40- 1 singlet-singlet, 40, 238-9, 564 triplet-triplet (see Triplet-triplet interaction) 1,1'-Binaphthyl, 124, (654) 2,2'-Binaphthyl, 124, (654) Bioluminescence, 599-600 Biphenyl (A), 26, 55, 75, 102, 104, 108, 123, 130, 179, 182, 212, 240, 261, 268, 276,281,426-7,433, 451 , 455,

460,464,466, 477-8,488,510,516,

527, 533, 548-50, 554-6, 593,

608-9,628,637,(652) Biphenyl'd lo (Ad), 26, 123, 130, 179,

182,451,488,609, (652) Biphenylene (C), 26, 75, 168-9, 182, 184,261,464,(652) Biphenylene oxide, 168 2-(4-Biphenyly1)-5-phenyloxazole (see BPO) 4-Biphenylylphenylether, 124, (655) Biphotonic processes (see Absorption, Photoionization) Birks-Conte model (energy migration and transfer), 584-90 Bisanthrene (8.1), 17, 74, 184, (651) Bis-(hydroxyethyl)-2,6-naphthalene dicarboxylate, 575, 612, (657) Bis-(isopropylstyryl)-benzene (see BPSB) 2,5 -Bis- [5 - t- butyl- benzoxazolyl (2)]thiophene (see BBOT) 1,4-Bis-[2-(4-methyl-5-phenyloxazolyl]benzene (see Dimethyl POPOP) 1,4-Bis-(trifluoromethyl)-benzene, 122, (642) Bisteroids, 596 Bond lengths, 2-3 BPO, 134, 136, 358,360, (653, 654) BPSB, 124, 135, 137, (653, 655) Born-Oppenheimer a pproximation, 47-8, 50, 149-50 p-Bromanil, 452, (655) Bromine, 412, 452, (655) Brominated fluoresceins, 102, 125, (655) 9-Bromoanthracene, 121, 322- 3, (646) 9-Bromo, lO-anthracene carboxylic acid, 121, (647) Bromobenzene,198,344, 368,436,458, 462, (643) 2-Bromobiphenyl, 261, (652) I-Bromo, 4-chloro-benzene, 257, (643) 1-Bromonaphthalene (2R), 22, 217,

257,264, 268, 286,605- 6, (644) 2-Bromonaphthalene (2V), 22, 217, 258, 271,449,635, (644) 9-Bromophenanthrene, 449 3-Bromopyrene (4.1E), 23, 180, 287, 352,357,362, (648) m-Bromotoluene, 458, (643) o-Bromotoluene, 458, (643)

Subject Index p-Bromotoluene, 458, (643) Butene-2, 242-3, 293, 630 9-iso-Butylanthracene, 121, (645) 9-n-Butylanthracene, 121, (645) 5-Butyl1 : 2-benzanthracene (4.35), 24, 358, (649) iso-Butyl benzene, 344, 368, 457, (642) n-Butylbenzene, 457, (642) sec-Butylbenzene, 122,457, (642) tert-Butylbenzene, 457, (642) Calibration, spectrometric, 97-8 Carbazole, 123, 235, 533, 597, 605, (655) Carbon disulphide, 213-14 Carbon tetra bromide, 443-4, 508, 584, 613, (655) Carbon tetrachloride, 213-14, 439-41, 444,485, (655) Carcinogenesis, 600 ,8-Carotene, 599, 627 Cata-condensed hydrocarbons, 3-4 (see also Individual compounds) Charge-resonance (excimer) states, 327-30, 343-7, 366, 421, 526-7, 625 Charge-transfer, absorption, 41, 403-15, 442, 447, 454-6,469,631-2,(661,665) contact absorption, 212, 412-15, 493-4, (665) interaction, 418, 425, 437 Chemiluminescence, 433 p-Chloranil, 35, 403-4, 408, 409, 412, 452-6,465-6,469,(655) Chlorine, 452, (655) 1-Chloroanthracene (3.IN), 23, 258, 272,319,362,485,577(646) 9-Chloroanthracene, 121, 322-3, 485, (646) 9-Chloro, lO-anthracene carboxylic acid, 121, (647) o-Chlorobenzaldehyde, 605, (655) p-Chlorobenzaldehyde, 605, (655) Chlorobenzene, 213, 268, 343-4, 368, 458,462,465, (642) 1-Chloronaphthalene (2Q), 22, 180, 213,217,257,264,286,605,(644) 2-Chloronaphthalene (2U), 22, 123, 217,257,270, (644) Chlorophyll, 599-600, 617, (655)

685 3-Chloropyrene (4.1D), 23, 352, 357, 362, (647) m-Chlorotoluene, 458, (642) o-Chlorotoluene, 458, 462, (642) p-Chlorotoluene, 122, 458, (643) Cholanthrene (4.3V), 24, 358, (649) Chrysene (4.4), 11, 25, 608, (649) absorption, 71,81,274-5,280,455, 459 electronic states, 71, 179, 184, 459, 463 excimer, 330, 367 fluorescence, 81, 123, 129, 133, 179, 231,235,252,476,502,511,533, 637 phosphorescence, 182, 228, 235, 259, 488,637 radiationless transitions, 179, 182, 185,187,201,231,235,252,287, 289 Chrysene·d 12 (4.4d), 25, 129, 182, 185-6,231,252,254,287,289,488, (649) Chrysoidin, 617, (655) Clar classification of absorption bands, 54-8 Collisional quenching (see Quenching, collisional) Complex, donor-acceptor (see Donor-acceptor complex) exchange (see Exchange complex) Concentration quenching (see Excimer formation and Quenching, concentration) Contact charge-transfer absorption, 212,412-15,493-4,496,(665) Contact exciplex, 435, (665-6) Copolymers, 598-9 Coronene (7.1), 16, 74, 77-8, 119, 130, .182,184-7,228,253,255,260,276, 281,287,363,374-5,455,460,463, 471,477,603, (651) Coronene·d 12 (7.1d), 130, 185-6,255, 287, (651) Coulombic interaction, 518, 520-1, 567-80,590-4 p-Cresol, 122, (655) Crystal (see also Exciton migration and transfer) defects, 319, 323, 339, 533-5

686

Crystal-continued excimer, 170, 317-19, 331-5, 339, 362-3, 534 growth, 530-1, 534 traps (see Exciton traps) types, 317-19 9-Cyanoanthracene (3.1M), 23, 319, 362,421,430-1,441,476,(646) 3-Cyanopyrene (4.1 F), 23, 352, 357, 362, (648) 2,2'-p-Cyclophane, 325, 345-7, 368, (655) 4,4'-p-Cyclophane, 325, 345-7, 368 Cytochrome C, 600 Cytosine, 325, 424-5, 600 complex (see Donor-acceptor complex) DA exciplex (see Exciplex, donoracceptor) Dansyl-(L-propyl)n-o:-naphthyl, 597-8 Dative bond wavefunction, 404-5 Davydov splitting, 34, 116, 318,523-8, (666) anthracene, 67-8, 526-7, 532, 566, 601, 611 benzene, 526, 546-7,635 naphthalene, 223-4, 526-7, 532, 635 phenanthrene, 532 theory, 523-8 Delayed fluorescence, 372-402, (662) crystal, 62-3, 215-16, 340, 544,559567, 635, (662) decay, 63,380-4 E-type, 32,145,164,235,373-8, (662) excimer, 36, 316, 373,380-4,541 excitation spectrum, 215-16, 527, 560-1,566,611,635 mixed crystals, 550-9 P-type, 36, 62-4, 215-16, 316, 338, 340,373,378-94,541-2,590-1, 598, 631-2, (662) recombination (see Recombination fluorescence) rigid solutions, 389-90, 590-1 sensitized P-type, 199, 373, 396-7, 542-4 spectrometry, 201-6 types, 372-3 vapours, 632 DA

Subject Index Delayed scintillation (see Scintillation, slow component) Deuteration, effect of, benzene tripiet, 248-50, 294-5, 545-7 energy levels, 107,249, 545 Sl - So internal conversion, 185 Sl - Tq intersystem crossing, 230-1, 286-7 T 1 - So intersystem crossing, 147-9, 155-8,182,248-50,294-5,418419,451,472-3,488,628 triplet-triplet energy transfer, 545-7 Dexter theory (see Energy transfer) 9,1O-Diacetoxyanthracene, 121, (646) 9-Diacetylaminoanthracene, 121, (647) Dianthracene, 320-3 Di-aromatic molecules, 163-4, 594-6 1:2:3:4-Dibenzanthracene (5.6), 12, 72, 77-8, 130, 180, 184, 186, 255, 260,268,275,281,287,358,363, 455,460,463,477, (650) 1 :2:5:6-Dibenzanthracene (5.7), 13, 73,130,133,181-2,184,186,252, 255, 260,276, 281, 287, 455, 460, 463,477, (650) 1: 2: 7: 8-Dibenzanthracene (5.8), 13, 73, 130, 133, 181, 184, 186, 255, 260, 287, 363, 455, 460, 463, 477, (650) 1 : 2: 7: 8~Dibenzochrysene (see 1: 2: 3 :4: 5: 6: 7: 8-Tetrabenzonaphthalene) Dibenzofuran, 594 2:3:8:9-Dibenzoperylene (7.3), 17, 133, (651) 1: 2: 3 :4-Dibenzophenanthrene (see 1: 2-Benzochrysene) (see 1 : 2: 5: 6-Dibenzophenanthrene 5 : 6-Benzochrysene) 2: 3: 5: 6-Dibenzophenanthrene (see 1 : 2-Benzotetraphene) 2: 3 : 7: 8-Dibenzophenanthrene (see 3: 4-Benzotetraphene) 3 :4: 5: 6-Dibenzophenanthrene (5.14), 4, 14, 73, 104, 133, 182, 184, 260, 463, (650) 1 :2: 3 : 4-Dibenzopyrene (6.14), 16, 260, 358,463, (651) 1: 2:4: 5-Dibenzopyrene (6.17), 455, 460,463, (651)

Subject Index

1: 2: 6: 7-Dibenzopyrene (6.11),15,133,

182,260, (651) 3 :4 :8 : 9-Dibenzopyrene (6.12), 16, 133, (651) 1:2:3:4-Dibenzotetracene (6. 15), 16, 363, (651) 1: 2: 7: 8-Dibenzotetracene (see Phenanthro-(3': 2': 2: 3)-phenanthrene) 2,5 -Di -(4- bi phenyly1)-1,3 ,4-oxadiazole (see BBD) 2,5-Di-(4-biphenylyl)-oxazole (see BBO) 9,1O-Dibromoanthracene, 121, 211, 213, 258, (646) 1,3-Dibromoazulene, 166 1,4-Dibromobenzene, 257, 343, 368, 527, (643) 1,4-Dibromonaphthalene, 217, 258, (645) 9,10 - Di - n - bromophenylanthracene, 121, (647) 1,5-Dichloroanthracene, 258, 449, (646) 1,1O-Dichloroanthracene, 258, (646) 9,1O-Dichloroanthracene (3.tH), 23,

120- 1,123,180,213,251,258,272, 362,424,440,475-6,485,508,514, (646) 1,2-Dichlorobenzene, 458, 462, 465, (642) 1,3-Dichlorobenzene, 458, (642) 1,4-Dichlorobenzene (lL), 21,256,458, 527, (642) 4,4'-Dichlorobiphenyl, 261, (652) Dichlorophthalic anhydride (DCPA), 418,471, (655) 2,5-Dichloroquinone, 469, (655) 9,1O-Dicyanoanthracene, 421 , 430--1, 476, (646) p-Dicyanobenzene, 476, 478, 633 Dielectric relaxation, 114-16, 165--6 p-Diethylaminobenzonitrile,164 Diethylaniline (DEA), 425-9, 437, 476-8, 484, (655) 1,2-Diethylbenzene, 457, (641) 1,3-Diethylbenzene, 457, (641) 1,4-Diethylbenzene, 344-5, 368, 457, (641) m-Difluorobenzene, 293, (642) o-Difluorobenzene, 292-3, (642) p-Difluorobenzene, 292-3, (642)

687 Diffusion coefficients, 481, 484, 509-13, 516, (667) Diffusion-controlled processes, 312--13, 434-5,441-7 excimer formation (see Excimer formation) exciplex formation (see Exciplex formation) impurity quenching (see Quenching, impurity) oxygen quenching (see Quenching, oxygen) singlet-singlet energy transfer, 36, 90-1, 434,576-80,588(667) triplet excimer formation, 347-8, 369,449-50, (666) triplet-triplet energy transfer, 538-

540, 607, (667) 9,1O-Dihydrophenanthrene, 637, (655) 4,5-Dihydropyrene, 259, (655) 1,5-Dihydroxynaphthalene, 258, (645) 2,7-Dihydroxynaphthalene, 258, (645) 1,4-Diiodobenzene,527 Dimer cation, 580-1, 630 Dimer, mixed, 543 Dimer, sandwich, 322-3, (666) Dimerization (see Photodimerization) 9,10-Dimethoxyanthracene, 121, 633, (646) p-Dimethylaminobenzonitrile, 164-5, 188, (656) I-Dimethylaminonaphthalene, 5-(or 7-) sodium sulphonate, 98 4-Dimethylamino-4' -nitrostil bene, 626 Dimethylaniline (DMA), 421, 425--6, 436--7, 476-7, 479, 484, 617, (656) 9,1O-Djmethylanthracene (3.1B), 22, 71, 121, 128, 179, 199,251, 310, 321, 341, 351, 356, 385- 6, 423, 475-6, 633, (645) 2',4-Dimethyl 1: 2-benzanthracene (4.3M), 24, 129, 358, (648) 2',6-Dimethyl 1 :2-benzanthracene (4.3N), 24, 129, 358, (648) 3',6-Dimethyl 1: 2-benzanthracene (4.3P), 24, 362, (649) 9,10-Dimethyl 1: 2-benzanthracene (4.30),24,129, 199,259,455,459, 600, (649) p,p'-Dimethylbiphenyl,433

688 1,3-Dimethyl, 4-ethyl, benzene, 344-5, 368, (642) 1,4-Dimethyl, 2-ethyl, benzene, 344-5, 368, (642) 1,2-Dimethylindole, 432 1,3-Dimethylindole, 480, (656) 1,2-Dimethylnaphthalene (2G), 22, 342,355,454,458,(644) 1,3-Dimethylnaphthalene (2H), 22, 355,454,458, (644) 1,4-Dimethylnaphthalene (21), 22, 355, 403,454,458, (644) 1,5-Dimethylnaphthalene (2J), 22, 355, 454, 458, (644) 1,6-Dimethylnaphthalene (2C), 21,127, 171,178,180,286,342,351,355, 360, 454, 458, (643) 1,7-Dimethylnaphthalene (2K), 22, 355, (644) 1,8-Dimethylnaphthalene (2L), 22, 355, 454, 458, (644) 2,3-Dimethylnaphthalene (2E), 22, 122, 127,178,355,430-1,454,458,476, 603. 609, (643) 2,6-Dimethylnaphthalene (2D), 21, 122, 127, 178, 351, 355, 454, 458, (643) 2,7-Dimethylnaphthalene (2F), 22, 355, 454, 458, (643) Dimethyl POPOP, 124, 135, 137, (653, 655) Dinaphtho-(2': 3': 3 : 4) (2: 3: 9: 10)pyrene (8.3), 17, 133, 603, (651) 9,10-Di-a-naphthylanthracene, 122, (647) 2,5-Di-(1-naphthyl) - 1,3,4-oxadiazole (see a-NND) 2,5 -Di -(2 -naphthyl) -1,3,4 -oxadiazole (see ,B-NND) 1,5-Dinitronaphthalene, 258 Dinucleotides, 325, 424-5 Diphenylacetylene, 268, (656) Diphenylalkanes, 324, 364-5, 595-6, (656) 9,1O-Diphenylanthracene (3 .1C), 22, 57,71,86,103-4,108, 120- 1,123, 128,179,251,258,317,322,341, 393, 440, 485, 508- 10, 514, 613, (645) 1,4-Diphenylbutadiene (see DPB) 1,I'-Diphenylethylene, 124, (656)

Subject Index 2,5-Diphenylfuran (see PPF) 1,6-Diphenyl 1,3,5-hexatriene (see DPH) Diphenylmethane, 124, 364, (656) Diphenylmethylene (DPM), 236-7 1,8-Diphenyll,3,5,7-octatetraene, 101-2, 120, (656) 2,5-Diphenyl 1,3,4-oxadiazole (see PPD) 2,5-Diphenyloxazole (see PPO) Diphenyloxide, 533 Diphenylpicrylhydrazyl (DPPH), 440 1,3-Diphenylpropane, 324, 364 Diphenylstilbene (see DPS) Dipole-dipole interaction, 518, 521, 528,568-80,593,597-8 Dipole moment, DA complex, 116,405,453, (665) excited molecule, 113-16, 165-6 excimer,478 exciplex, 428, 478 9,1 O-Di-n-propylanthracene (3.1 G), 23, 121,321,352,356,423,475-6, (645) Ditolylalkanes, 324, 365 9,10-Di-m-tolylanthracene, 121, (645) 9,1O-Di-n-tolylanthracene, 121, (645) 9,1O-Di-o-tolylanthracene, 121, (645) DNA, 425, 600 Donor-acceptor (DA) complex, 403420,453 absorption (see Charge-transfer absprption) binding energy, 411-14, 465- 6, (665) contact, 212, 412- 15, 493-4, 496, (665) dipole moment, 116,405,453, (665) dissociation, 41, 397,410,416, (666) extinction coefficient, 407, 410-12, 442,454-5 formation, 34-5, 163, 403, 442, 599600 (665) fluorescence, 35, 163. 415-16, 418, 468-9, 632, (662) internal quenching, 41, 435- 7, (663) intersystem crossing, 41, 416, 436-7, (664) phosphorescence, 35, 163, 416-20, 470-4, 631-2. (663) potential energy diagram, 406-7, 411 reaction kinetics. 410-12 theory, 404-15

Subject Index Doubly-excited (excimer) states, 327, 366, 394 DPB, 120, 268, 603, (656) D PH, 101,120, 124, 603, (656) DPS, 135, 137, (653, 656) Durene OK), 21, 256, 269, 416-17, 419, 453-4, 457, 465, 468-71, 474, 476, 478, 527, 557, (641) Dye laser, 69 Dye luminescence, 164,372-8 D ynamic quenching (see Quenching, dynamic) Einstein, coefficients, 48-52, 85-7, 150 relation (radiation), 48 unit, 89 Electrochemiluminescence, 340-2, (662) Electron, affinity, 347,404, 406- 9, 427- 8, 434, 452,462-4, (666) beam excitation, 29, 216-18, 224, 342-5 exchange interaction, 512- 13, 518521,538-9,544,546-8,567- 70, 576, 586, 592, 598 orbitals, 2-3 spin resonance, 199-200, 449, 540, 549-51 transfer, 240, 403-15, 429-30, 437-8, 599 Electronic, configuration, 1-3 factor, 150-1, 160- 1, 230-4, 289 structure, 1-10 Energy gaps, 159-60, 168, 184,608- 9 Energy migration (see also Exciton migration) collisional, 518-20, 584- 90 Coulombic, 12, 518,520-1 electron-exchange, 112, 390,518-21 higher excited states, 174, 589, 593 intramolecular, 518,597-600, (667) liquids, 36, 174, 580-90, 614, 635, (667) polymers, 171 , 339, 518,572,597-9, 636 radiative, 92- 3, 518-23, 531- 2, 536-7, (667) singlet-singlet, 39, 112, 143,518-22,

689 Energy migration-continued 580-90,614,(667) singlet + triplet, 39, 521, 590 triplet-triplet, 39, 390, 519-20, 598, 631-2, 635, (667) triplet + triplet, 39, 390, 520- 1, 543, 590 types, 34- 5, 39,518-21 Energy transfer (see also Exciton transfer) collisional, 36, 518-20, 540, 584-90 Coulombic, 518, 520- 1, 567- 80, 590-4 Dexter theory, 539,569- 70 diffusion, influence of, 36, 540 electron-exchange, 518-21, 537-44, 567-70, 635 excimer, 338, 582 fluid solutions, 173-4, 538-41, 570580,613, (667) Forster theory, 567-76, 579-80, 585-6, 591 higher excited states, 174, 529, 533, 593-4 intramolecular, 164, 518, 594-600, 626, (667) polymers, 171, 572-4, 597-9, 636 radiative, 90- 1, 518- 23, 529, 534, 536-7,576-7, 593, (667) singlet-singlet, 39, 90-1,435,519- 23, 567-90,595-7,612- 3,636,(667) singlet + triplet, 39, 521, 569, 590, 592-3 triplet-singlet, 39, 206-7, 519- 20, 523,590-1, 617- 18, (667) triplet-triplet, 39, 240, 519-20, 537544,595-8,605- 7,635(667) triplet + triplet, 39, 492, 521, 543, 569,590- 2 types,34-5,39,518- 21 vibrational, 110- 12 Energy units, 47 Environmental effects (see Solvent effects, Refractive index) Eosin, 32, 373-4 2-Ethoxynaphthalene, 258, 271, 322, (645) 9-Ethylanthracene (3.1 E), 23, 121, 251, 321 , (645) 5-Ethyll : 2-benzanthracene (4.3Q), 24, 358, (649)

690 10-Ethyl 1: 2-benzanthracene, 259, (649) Ethylbenzene (lH), 21, 122, 126, 178, 256,342,354,457,(641) 9-Ethyl, lO-bromoanthracene, 121, (646) Ethyl bromide, 209 6-Ethylchrysene, 476, (649) Ethyl dichloroacetate, 482, (656) Ethyl iodide, 213-14, 444, 606, (656) Ethyl isothiocyanate, 482, (656) Ethyl monochloroacetate, 482, (656) 1-Ethylnaphthalene (2N), 22, 338,355, 598, (644) 2-Ethylnaphthalene (2Q), 22, 342,355, 454, 458, (644) p-Ethyltoluene, 122, (642) Ethyl trichloroacetate, 482, (657) Ethylene bromide, 213-14 E-type delayed fluorescence (see Delayed fluorescence, E-type) Exchange complex, 493-4, 496- 7, 512513,635 Exchange quenching (see Quenching, exchange) Excimer, 301-71 absorption, 40, 62, 335-6, 628, (661) binding energy, 312, 327, 354- 8, 587, (665) crystal, 170, 317-19, 331-5, 339, 362- 3 dissociation, 40, 303, 312-16, 337-8, 351-2, 519-20, 581, 587-8, 615, (666) enthalpy, 309, 312, 325, 354-8, (665) entropy, 309, 312, 325,354-8, (665) fluorescence, 35, 162-3, 301-42, (662) delayed (see Delayed fluorescence, excimer) internal quenching, 40, 337, 351-2, (662) lifetime, 95-6, 303, 311, 351-2, 635-6, (662) polarization, 335 quantum efficiency, 301-3, 309, 351-2, (662) quantum yield, 100, 301-4, 307, 309, 364-5, 379, 381, 386-7, 395- 6,400,629, (662) response function, 95-6, 305c-6, 310-11

Subject Index

Excimer-continued spectrum, 99- 100, 176, 301-2, 316-19, 323, 326-7, 331-6, 342, 354-8, 362-5, 478, 626, 629-30, (662) formation, 35,40,91-2,301-3,312322, 339-42, 349- 52, 39]-2, 519-20, 564, 580-1 , 587- 8, 615, (665-6) high temperature behaviour, 309-11, 386 higher excited states, 175-6, 366, 629-30, (666) impurity quenching, 338 interaction potential, 316-17, 319, 325-35,420,427,587 internal conversion, 40, 175-6, 190, 307, 337, 351-2, 581-2, (663) intersystem crossing, 40, 307, (664) intramolecular, 164, 171, 323-5, 364-5,595-6, (662,665) intermolecular mixed, 324, 365, 424, 475, (662) low temperature behaviour, 313-14, 386 mixed, 420-5, 475, 521, (662, 665) molar equilibrium constant, 309-11, 587-8,615 phosphorescence, 40, 163, 335- 6, 342-8,368,373,629-31, (663) polymer, 116, ] 71, 325, 339, 572, 629 potential energy diagram, 325-7, 331-5 quintet state, 366, 394 radiative lifetime, 309-10, 336, 351- 2,636, (662) rate parameters, 40, 302-9, 337, 351- 2,379,(665-6) reaction kinetics, photostationary, 302-4, 309-12, 378-9 transient, 304-11, 380-4 steric hindrance, 317, 321-2, 324, 588 theory, 327-35,345-7, 366-7, 420 thermodynamics, 309,312,315-16 triplet state, 40, ] 63, 335-6, 342-8, 366, 368, 394, 627-8, 630-1 , (663,666) triplet quantum yield, 307, 337-8, 379,627

Subject Index Exciplex, 420-33 acceptor-donor (AD), 420-1, 42530,478-9 binding energy, 424, 435, 632- 3 contact, 435 definition, 35, 420 dipole moment, 428, 478, 632-3 dissociation, 41,397,437-8,447,483, 498- 9,519- 21,542-3, (666) donor-acceptor (DA), 421, 426-8, 430- 1,478 fluorescence, 35, 41, 163, 166, 171, 425- 33,476-80,483,632,(662) lifetime, 429-30, 479, (662) quantum efficiency, 428, 479, (662) quantum yield, 421-3, 426, 42830,436 spectrum, 423, 425- 8, 430, 432, 476-80, (662) formation, 35, 41, 101, 163, 338, 421 - 2, 428- 32, 447, 483, 498500, 519-21, 542-3, 626 (665) internal conversion, 41, 435-6, 479, 483,498-502,508,(663) intersystem crossing, 41, 436-8, 483, 498-502, 508, (664) intramolecular, 164, 171, 424- 5, (665) phosphorescence, 41, 163, 171, 436, 483 radiative lifetime, 430, 432, 438- 9, 479, (662) rate parameters, 41, 428-32, 435-7, 479,483, (665) theory, 420,427 triple, 633 Excitation migration (see Energy migration, Exciton migration) Excitation transfer (see Energy transfer, Exciton transfer) Exciton, band model, 524- 9, 535 excimer, 338 fission, 40, 564 hopping model, 528-32, 544, 566 interaction, singlet-singlet, 40, 238 triplet-triplet (see Triplet-triplet interaction) lifetime, 529- 33, 544 localized, 528-9

691

Exciton-continued migration (see also Energy migration) singlet, 35- 6, 319, 339, 528-37, 547,586,604,(666) triplet, 35, 62-3, 528,544-50,559567, (667) phonon interaction, 528, 535, 566 resonance (excimer) states, 327- 30, 334- 5,345-7,366,421 singlet, 170,528-37,544,564 spectral shift, 116, 525, 527-8, 602, (667) splitting (see Davydov splitting) states, 170, 523-8 theory, 523-8 transfer (see also Energy transfer) singlet, 39, 529- 37, 586, 603, (667) triplet, 39, 544- 59, 608-9, 635, (667) traps, 530,533- 5, 550-9,562-3,567 triplet, 170, 528, 533, 544-67, 610~1l, (667) Extinction coefficient, 46-7, 58-9, (660) (see also Absorption) Factor-group splitting (see Davydov splitting) Ferrocene, 170 Flash photolysis, 10, 58-62, 76-8, 196-7,219,225-6,540-1,581,625, 628, (660) Fluoranthene (F), 26, 75,81,104,123, 131, 169- 70, 179, 182, 184, 253, 261,385,388,460,477,533, (652) Fluorene (B), 26, 75, 81, 108, 123, 130, 179,182,184,212,235,253,261, 268,277,281,460,477,502,511, 533,603,637, (652) Fluorescein, 93,102,120,125, 207,254, 376, (657) Fluorescence (Sl - So unless otherwise stated), anomalous,31-2,69,166-8, 171,627 crystal, 62-9, 170,317- 9,331-5,339, 362-3,528-37,545-6 DA complex (see DA complex fluorescence) definition, 31 delayed (see Delayed fluorescence)

692

Fluorescence-continued dual, 118- 19, 162-71, (661) dye, 164,373-8 environmental effects (see Refractive index, Solvent effects) excimer (see Excimer fluorescence) exciplex (see Exciplex fluorescence) excitation spectrum, 171-7, 241-8, 292, 376-8 external quenching (see Quenching) internal quenching, 32, 145-7, 178181,229- 35,246-8,(661) lifetime, 31, 49, 62, 89, 103-9, 115, 120-31, 136- 7, 142, 145, 229, 236,243-4,311,351-2,445,522, 529-32, 585- 6,589-90,616,626, 635-6,638, (661) lifetime determination (see Fluorometry) parameters, 88-9, 193 polymer, 116,170-1,325, 5YJ QI - Qo, 237, (661) quantum efficiency, 85, 89,108 , 120131,136- 7,142,145,229,251-3, 351-2, (661) quantum yield, 90-3,98,111,171-7, 200,209- 11,229,234--5, 241-8, 251-4,264, 266,292, 301-3,307, 309, 364- 5,377-8,379,395,400, 439- 41, 445, 522, 530, 571, 585-6,627, 637-8, (661) quantum yield determination, 93, 97, 100-2 radiative lifetime, 55, 87-8, 100-6, 120-31, 178-9, 186, 244, 626, 636, (661) reaction kinetics, 88-92 recombination (see Recombination fluorescence) resonance, 88, 111,247 response function, 89, 94-6, 304, 310-11,570-1,574-5,577-9 saturated hydrocarbons, 636, 638 scintillator solutes, 108-9, 134-7 self-quenching (see Excimer formation; Quenching, concentration) spectrometry, 97-100 spectrum, 48, 54, 62-4, 84-7, 97-100, 105-19, 133, 136-8, 142, 241, 247,265,364-5,376- 8,522,534, 627-8,638, (661)

Subject Index

Fluorescence-continued Sp - So, 31, 38, 123, 131, 143-4, 162, 166-8,179,236,627, (661) Sp - SI, 32, 161 TI - To, 236, (661) Tq - TI, 31, 38, 167, 193, 235-7, 627-8, (661) vapour, 84, 109-14, 138, 240-8, 292-3 Fluorobenzene, 122, 171, 212, 268, 292- 3,457,462,496,(642) Fluorocarbon solvents, 117-18 Fluorometry, modulation, 94-5, 305-6, 577 phase, 94-5, 109,243,305-6,577 photon-sampling, 96-7, 109, 204, 305-6 pulse, 95-6, 102, 109,305 1-Fluorohaphthalene (2P), 22, 251,257, 264,286,356, (644) 2-Fluoronaphthalene (2T), 22, 257, 356, (644) Folacin, 600 Forster kinetics, 570-80,591,593 Forster theory (see Energy transfer) Franck-Condon, envelope, 52-4, 116, 158 factor, 148, 150-62,230-1, 289, 451, 527,568,586 maximum, 52-4, 109, 113-16, 326 principle, 51-4, 11 3-16, 165, 332 Free radical formation, 439-41 Fuchsin, 617, (657) Fulvene, 173,246-7,628-9 G-values, 581-2 Glow curve, 398 Graphite, 464, (657) Ground-state deplation, 58-9, 196-7 Guanine, 600 Haem, 600 Haemoglobin, 600 Hafner's hydrocarbons, 166 Ham band, 175 Harmonic oscillators, 45, 52-3, 153-5, 332-4 Heavy-atom effect, atoms, 208-9 DA complexes, 418-20, 436, 472-3

Subject Index Heavy-atom effect- continued external, 167, 197-8, 209-14, 236, 266-7,436-7,447-8, (663-4) general, 8, 35, 208-11 internal, 35, 107, 209- 11, 213, 230, 233,264-5,538, (663-4) Helicenes, 4, 104-6 (see also Individual compounds) Heptahelicene (7.2), 4, 17, 104-6, 130, 179, (651) 'Hetero-excimer', 421 (see Exciplex; Excimer, mixed) 1: 12:2: 3 :4: 5: 6: 7:8:9: 10: ll -Hexabenzocoronene (13 .1), 19, 182, 261, (652) Hexacene (6.5), 3, 14, 74, (650) Hexachlorobenzene (10), 21, 257, (643) Hexaethylbenzene, 465, (641) Hexafluorobenzene,292- 3,458,(642) Hexahelicene (6.8), 4, 15, 74, 104-6,

130,179,182,184,235,260, (650) 1,2,3,6,7,8-Hexahydropyrene, 258, (657) Hexamethylbenzene (1F), 20, 126, 178, 256, 269, 415, 417, 419, 430-1, 453-4, 457, 465, 468, 470-1, 474, 476,632, (641) Hexaphene (6.7),15, 74,184, (650) Hopping model (see Exciton hopping model) Hormones, 600 Hot bands, 45-6, 223, 540 Hydridization, 1- 3, 320-1 2-Hydroxynaphthalene, 258, (645) 2-(0- Hydroxyphenyl) - benzimadazole, 169 Hypsochromic shift, 107 Impurity quenching (see Quenching, impurity) Individual compounds, 641-59 Individual processes and parameters,

660-7 Indole, 431-3,480,626, (657) 'Inner filter' effect (see Self absorption) Internal conversion, benzene derivatives, 146, 161-2, 171-7, 185, 187, 189- 90, 234, 245- 8,581- 2,636, (663) DA complex, 41, 435-7

693 Internal conversion-continued definition, 31 excimer, 40, 175-6, 190, 307, 337, 351-2,581-2,(663) exciplex, 41, 435-6, 479, 483, 498502,508, (663) SI - So, 32, 38, 146-7, 159-61, 167, 185, 196, 200-1, 229, 245, 248, 627, 636, (663) Sp - S1, 32, 38, 111- 12, 142-4, 147, 159, 161-2, 166, 171-7, 187,

189-90,234-5,529, 581- 2,(663) Tq - T 1 , 32, 38, 145, 147, 169, 193,

214,235- 7,594,(663) Internal quenching, 32, 42, 110-11, 145-7, 167, 178-81,312, (661) (see also Internal conversion, Intersystem crossing) Intersystem crossing, DA complex, 41, 416, 436-7, (664) definition, 31 excimer, 40,307 (664) exciplex, 41, 436-8, 483, 498-502, 508, (664) heavy-atom effect (see Heavy-atom effect) SI - T 1 , 32,38,144- 7,159,193,196, 209-1 1,229-35,289, (664) SI - T q , 32,38,144-7,160,167,193, 231-5,264,266,286- 7,289,447, 547,561,626-7,636,(664) Sp - T q , 32, 38, 167,234-6, (664) Tl - So, 32, 38, 147-59, 167, 182, 193-6, 209- 11, 226, 255, 264, 266, 294, 296, 374, 418-20, 447-8, 451, 473, 628-9, 633, (664) Tl - S1, 32,38,144-5,235,374, (664) Tq - S1, 38, 145, 193,235, 390, 591, (664) p-Iodanil, 452, (657) Iodinated fluoresceins, 125, (657) Iodine, 404, 412, 452- 6, 465-6, 606, (657) Iodine chloride, 452, (657) m-Iodobenzaldehyde, 605, (657) Iodobenzene,344,368,458,(643) 2-Iodobiphenyl, 261, (652) Iodochlorofluorescein, 125, (657) 1-Iodonaphthalene (2S), 22, 217, 233,

257,264,286,511,605- 6, (644)

694

Subject Index

2-Iodonaphthalene (2W), 22, 217, 258, (644)

m-Iodotoluene, 458, (643) o-Iodotoluene, 458, (643) p-Iodotoluene, 458, (643) Ion recombination, 40, 397-8, 580-1 Ionization potential, 33-4, 237-8, 290, 347,406-9,457-60, (666) (see also Photoionization) Ionization quenching (see Quenching, ionization) Isomerization (see Photoisomerization) Isoquinoline, 268, (657) Isotope rule, 155- 8 (see also Deuteration, effect of) Isoviolanthrene, 603, (657) Kasha's rule, 144-5, 161- 71, 236-7 Lasers, applications of, argon ion, 69 dye, 69 frequency-doubling, 60- 1, 76 neodyrrlium, 60-1,67,69, 79, 166 nitrogen, 69, 630 Q-switching, 60, 69 ruby, 60-4, 67-8, 76, 79, 166, 560, 563,625 Light sources, 76, (660) N-Lithium carbazole, 398-9 Lithium diphenylamide, 398 Mercury emission lines, 291,339 Mesitylene (IE), 20,70,122,126,17], 178, 256, 342, 354, 408, 417, 440, 457,465, 470, 581, 584-5, 613-16, 625, 629, (641) 9-Methoxyanthracene (3.11), 23, 121, 321,356, (646) 9-Methoxy, 1O-bromoanthracene, 121, (647) 9-Methoxy, 10-chloroanthracene, 121, (647) ]-Methoxynaphthalene (2X), 22, 127, 178,200,251,322, (644) 2-Methoxynaphthalene (2Y), 22, 127, 178,322,430,476,(644) N-Methyl acridinium chloride, 120, (657) 3-Methylarrlinophthalimide, 110-11, 138, (657) p -Methylanisole, 122, (657)

1-Methylanthracene, 321, 629 9-Methylanthracene(3.1A), 22,71,121, 123,128,179,181,251,268,310, 321- 3,356,385,431,475,485,594, 617, 629, (645) 9-Methylanthracene'd 12 (3.1Ad), 22, 181, (645) l'-Methyl 1 :2-benzanthracene (4.3A), 24, 259, (648) 2' -Methyl 1: 2-benzanthracene (4.3B), 24,129,259,357,454,459, (648) 3' -Methyl 1: 2-benzanthracene (4.3C), 24,129,259,357,454,459, (648) 4'-Methyl 1 :2-benzanthracene (4.3D), 24,129,259,357,454,459, (648) 3-Methyl 1: 2-benzanthracene (4.3E), 24,129,259,357,454,459,(648) 4-Methyl 1: 2-benzanthracene (4.3F), 24,129,259,357,454,459, (648) 5-Methyl 1 :2-benzanthracene (4.3G), 24,99,129,179,259,349,352,357, 362, 385,454,459,475,632, (648) 6-Methyl 1: 2-benzanthracene (4.3H) 24, 129, 179, 259, 349, 352, 357, 362, 454,459,475, (648) 7-Methyl I :2-benzanthracene (4.31), 24,129,259,357,454,459, (648) 8-Methyl 1: 2-benzanthracene (4.31), 24,129,259,357,362, (648) 9-Methyl 1: 2-benzanthracene (4.3K), 24,129,259,357, (648) 1O··Methyl 1 : 2-benzanthracene (4.3L), 24, 129, 179, 259, 349, 352, 357, 455,459, (648) I-Methyl 3 :4-benzophenanthrene (4.5A), 25, 260, 362, (649) 2-Methyl 3: 4-benzophenanthrene (4.5B), 25, 260, (649) 5-Methyl 3 :4-benzophenanthrene (4.5C), 25, 260, (649) 6-Methyl 3 :4-benzophenanthrene (4.5D), 25, 260, (649) 7-Methyl 3 :4-benzophenanthrene (4.5E), 25, 260, (649) 8-Methyl 3 :4-benzophenanthrene (4.5F), 25, 260, (649) 4-Methyl biphenyl, 123, 433, (652) 9-Methyl, 1O-bromoanthracene, 121, (646) 20-Methylcholanthrene (4.3W), 24, 362, (649)

Subject Index Methyl dithiomethane, 482, (657) 9-Methyl, lO-ethylanthracene, 121, 321, (645) I-Methyl, 4-ethylbenzene, 122, (642) I-Methylindole, 480, (657) 9-Methyl, 10-methoxyanthracene (3.11),23,121 ,321,356, (646) 1-Methylnaphthalene (2A), 21,70,122, 127,178,181,209,251,257,264,

270,286, 342,351,354,360,408, 455, 458, 466, 594, 605, 630, 632, 635, (643) 2-Methylnaphthalene (2B), 21,70,122, 127, 171, 176,178,181,189,251,

257,351,354,360,455,458,466, 530,534,558,603,632, (643) 2-Methylnaphthalene'd 1o (2Bd), 550-1 1-Methylphenanthrene, 609, (647) Methylphenylsulphone, 268, (657) 1-Methylpyrene (4.JA), 23, 357, 420-2, 475, (647) 3-Methylpyrene (4.IB), 23, 357, (647) 4-Methylpyrene (4.1C), 23, 352, 357, 362,475, (647) 4-Methylquinoline, 268, (657) 4-Methyl terphenyl, 123, (652) Methyl thiomethane, 482, (657) Mirror symmetry relation, 85-7, 100-3, 106, 113-16, 144, 217-18, 415416 Mixed dimer (see Dimer, mixed) Mixed excimer (see Excimer, mixed) Mixed sandwich dimer (see Sandwich dimer, mixed) Modulation fluorometry, 94-5, 305-6,

577 Molecular orbitals, 1-3 Molecular structure, 3- 4, 11-27, 134-5,

(660) 'Moloxide' hypothesis, 503 9-Monacetylaminoanthracene, 121, (647) Monoisopropyl biphenyl, J23, (652) Mulliken model (DA complexes), 404413,439,496 Multiphotonic absorption, 32-4, 38,

62-9,79-81,561,625,(660) Multiplet structure, 118-19 Multiplicity, 8,151,161,216,581 Multipole-multipole interaction (see Coulombic interaction)

695 Murrell model (DA complexes), 413415,439,494, 496 Myoglobin, 600 Naphthacene (see Tetracene) 2-Naphthaldehyde, 258, (657) Naphthalene (2),3-4,11,21, (643) absorption, 46, 56, 58,62,64,67,70,

77-8,80,118 , 215,217- 18,220, 223-6, 232, 269-70, 280, 284, 526, 591-2,635 crystal, 64, 170, 215, 223-4, 362, 524-7, 529- 30,532-5,544,547-

51,555,557-9,603,608-9,635 Davydov splitting, 170,223-4,524-7, 532,635 delayed fluorescence, 215, 385, 389, 398,433,555,557-9,592, 632 diffusion, 510- 11, 516 donor-acceptor complex, 414-19, 453-4,458,465,468- 73 electronic states, 7-10, 62, 70, 78, 104,170,184,216,223-4,225-6, 232-3, 284, 290, 409, 458, 462, 526-7 energy (or exciton) migration and transfer, 529, 533-7, 548-51,

554-5,603-6,608-9,635 excimer, 163, 330, 347-8, 351, 354, 362,367-9,385,450,630-2 excipIex, 427, 431, 476, 632-3 fluorescence, 31, 106-7, 118, 122, 126,133,146,171,177,178,186, 208-11, 235-6, 251, 254, 264, 266,286,351,354,398, 419,433, 530,532-5,544,579,595,597 impurity quenching, 440, 448-51, 486,502,506,511,513,544,579 phosphorescence, 163,182, 186,208211,217-18,228,254, 257,264, 266, 284, 347-8, 368, 398, 416,

419,470-3,537-8, 544, 547,555, 591-2,597,631 ,633 radiationless transitions, 146, 161,

171,177,178,180,182,185, 187, 200, 208- 11, 232-3, 235, 251, 254,264,266,286,289,351,418419,473 triplet lifetime, 182, 254, 264, 266-7, 347-8,369,418-19,448-51,488, 506,549-50,628,633

696

Subject Index

Naphthalene · dB(2d), 21, 122, 126, 178,

180,182,185-6,211,222,235,251, 254, 25~ 26~ 280, 286, 289, 418-

a-NPO, 124, 134, 136, 358, 360, (653, 658)

419, 449, 451 , 472-3, 487-8, 540,

550-1,558-9, 598,607-9,(643) I-Naphthalene sulphonic acid, 270, (645) 1-Naphthoic acid, 258, (645) 2-Naphthoic acid, 258, (645) I-Naphthol, 123, 270, (644) 2-Naphthol, 123,459, (644) Naphtho-(2': 3': 3 :4)-pyrene (6.13),16, 133, (651) 1-Naphthylamine, 123, 459, 466, 609, 626, (644) 2-Naphthylamine, 459, 466, 626, (645) I-Naphthyl, 9-anthryl alkanes, 594-5 I-Naphthyl, p-benzophenone alkanes, 595 2-Naphthyl methylketone, 617, (657) 2-(l-Naphthyl)-5-phenyl 1,3,4-oxadiazo Ie (see a-NPD) 2-(2-Naphthyl)-5-phenyll,3,4-oxadiazole (see ,8-NPD) 2-(l-Naphthyl)-5-phenyloxazole (see a-NPO) Neodymium laser, 60-1, 67, 69, 79,166 Nicotinic acid, 600 Nitric oxide, 452, 492-513, (658) contact cr absorption, 452, 493-4, (666) exchange complexes, 49J-c5, 505, (665) fluorescence quenching, 110, 442, 493,504-8, (666) induced So - T q absorption, 212, 242,283,493,496,625,(666) triplet quenching, 442, 447- 9, 493, 504- 8, (666) 9-Nitroanthracene, 268, (647) 1-Nitroazulene, 166 Nitrogen laser, 69, 630 Nitromethane, 482, (658) a-NND, 124, 135, 137, (653, 656) ,8-NND, 124, 135, 137, (653, 656) No-bond wavefunction, 404-5 Nonahelicene (9.2), 4, 18, 104-6, 130, 179, (651) a-NPD, 124, 134, 136, 358, (653, 657) ,8-NPD, 134, 136, 360, (653, 657)

Octafluorotoluene, 458, (642) Octahelicene (8.2), 4, 17, 104-6, 130, 179, (651) Octupole-octupole interaction, 526, 570,586 Onsager, dielectric theory, 113-16 o - 0 transition, 46, 52-3, 55, 106, 113-16,208,218,563 Orbital ring quantum number, 6 'Oriented gas' model, 523-4 Oscillator strength, CT absorption, 410 molecular, 51- 2, 67, 110, 138, (660) Ovalene (10.1), 18, 75, 184, 363, 603, (651) l-a-Oxyethylanthracene, 475, (646) 9-a-Oxyethylanthracene, 475, (646) Oxygen, 452,492-513,(658) contact CT absorption, 211,412-13, 452,492,493-4, (666) diffusion, 510-11, 515 exchange complexes, 493-4, 496-7, 512- 3, 635, (665) excited states, 492, 634 fluorescence quenching, 35, 90-1, 110,173,442,444, 492,496-510, 514-15,584,613,635,(666) induced So - Tq absorption, 211-12, 223, 242, 268, 283, 412, 492,

494-6, (660, 666) photoperoxidation, 198-9, 492, 501, 502-4,634, (667) removal, 90-1, 206 singlet-excited, 198-9, 492, 501-4, 599-600,634 triplet quenching, 206, 344, 442, 447-9,492,500-4,599,(666) Paramagnetic ions, 447- 9, 486- 7, 495 Paramagnetic molecules (see Nitric oxide, Oxygen) Pariser model (electronic states), 10, 67-8,224-8,232-3,283-5 Parity, 9-10, 61-2, 65-8, 151 , 161,222, 224-8, 234 p-bands, 54-8, 105, 143,525-7,601- 2

Subject Index PBD, 124, 135, 137, 440, 585,613, (653, 658) Pentacene (5.4), 3, 12, 56, 72, 184, 238,

275,281,317,330,460,463,603, (650) Pentafluorobenzene, 457, (642) Pentamethylbenzene, 3, 14, 73, 184, 454,457, (641) Pentaphene (5.15),260,463, (650) n-Pentylbenzene, 344, 368, (642) Perfluoroheptane, 117-18 Peri-condensed hydrocarbons, 3-4 (see Individual compounds) Perrin relation, 441 (see 'Active sphere' model) Perylene (5.1),12,290,635, (649) absorption, 72,81,86,92,238,275,

437- 8,455,460,527 crystal, 238, 316,362,425,460, 527,

603 delayed fluorescence, 396-7, 543 electronic states, 72, 179, 184, 460, 463 excimer, 316,341,358,362,421,425, 629 fluorescence, 81, 86, 92, 120, 123,

129-30,133,179,231,252,341, 358,362,425-6,436-8,477,484,

505-9,514,577,592- 3,603 radiationless transitions, 179, 185, 199,201,231,240,252,287,289 Perylene ' d 12 (5.1d), 130, 185, 187, (649) PFEO model (electronic states), 4-10,

54-6,62,70-5,78,208,224-8 Phase fluorometry, 94-5, 109, 243, 305--6, 577 Phenanthrene (3.2),3-4,11,23,239-40,

466,605-6,609,635, (647) absorption, 57, 71,77- 8,81,222,268,

272, 280,454,459,469 crystal, 532, 533, 554-7, 603-4, 608 delayed fluorescence, 341, 385, 389, 554-7,592,632 . electronic states, 7, 71, 78, 184, 259, 459,462,532 excimer, 330, 341, 347-8, 367, 369, 450 fluorescence, 81, 104, 128, 133, 179, 186,231,252,254,341,430-1, 440, 468-9, 476, 502, 511, 532,

533,575,578-9,603-4

697

Phenanthrene-continued phosphorescence, 182, 186, 228, 254, 259,347- 8,369,416-19,450-1, 470-3,488, 554-5,631 radiationless transitions, 179, 182, 185,187,201,231,235,252,254, 286,289,418- 19,451 Phenanthrene·d lo (3.2d), 23, 128, 182, 185, 222, 252, 254, 259, 272, 280, 287,290,418-19,472-3,488,540, 548-50,554-6,591-3,607-9,618, 635, (647) Phenanthridine, 268, (658) Phenanthro-(3': 2': 2: 3)-phenanthrene (6.10), 15, 133,463, (650) Phenanthro-(3': 2': 3 :4)-pyrene (7.4), 17, 133, (651) Phenazine, 603, (658) Phenes, 3-4, 57-8 (see also Individual compounds) Phenol, 122, 398, (658) Phenylacetylene, 268, (658) Phenylalanine, 600 9-Phenylanthracene (3.1D), 22, 121, 123, 128, 179, 251, 321, 385, 485, (645) 2-Phenylazulene, 166 p-Phenylbenzaldehyde, 617, (658) 2-Phenyl, 5-(4-biphenylyl)-1,3,4-oxadiazole (see PBD) 9-Phenyl, 10-bromoanthracene, 121, (646) Phenylcyclohexane, 122, (658) Phenylcyc/opropane, 268, (658) Phenylether, 124, (658) 3-Phenylfluoranthene, 123, (652) 1-Phenyl naphthalene, 258, (644) 2-Phenylnaphthalene, 169,258, (644) 9-Phenyl, 1O-cx-naphthylanthracene, 121, (647) Phenyl-tolyl alkanes, 364-5, (658) m - Phenylene - bis - phenylmethylene (TPM), 236-7 Pheophytin, 617, (658) unless Phosphorescence (TI - So, otherwise stated) DA complex (see DA complex phosphorescence) decay, 194-5 (see also Triplet state lifetime) definition, 31, 194-5, 372-3

698

Phosphorescence-continued excimer (see Excimer phosphorescence) exciplex (see Exciplex phosphorescence) excitation spectrum, 214-5, 635 lifetime (see Triplet state lifetime) mixed crystals, 547-59 QI - To, 236 quantum efficiency, 147, 167, 194-5, 207-8, 254-5, 264, 266, 448, 562- 3, (663) quantum efficiency determination, 206-7,211 ,591 quantum yield, 194-6, 234---5, 254, 264-6, 374-5, 382-4, 538, 544, 547, 592-3, (663) quantum yield determination, 205206 radiative lifetime, 88, 167, 186, 211, 218,227-8,233,254-5,264,266, 418- 19,448,451,473,(663) reaction kinetics, 194-5,214 recombination (see Recombination phosphorescence) spectra, 148- 9, 156-7, 166-7, 182, 194, 207-8, 217-18, 222, 249, 256-61, 265, 346, 367, 374---5, 417- 18, 562- 3, 591, 599, 627, (663) spectrometry, 201-6 SI - Qo, 237 SI - To, 236 T 1 - Qo, 237 Tq - So, 31-2, 38,167-70 Phosphorimetry, 201-6 Photobiology, 29, 599-600 Photocarcinogenesis, 600 Photochemical quenching, 439-41, 485, (667) Photochemistry, 29, 599 (see also Individual processes and parameters) Photoconductivity, 238-9 Photodimerization, 317, 319-22, 338, 439, 542, 599-600, 629, 633, (665, 667) Photodynamic action, 600 Photoionization, biphotonic, 34, 38, 238-9, 397-9, 599, (666)

Subject Index

Photoionization-continued direct, 38, 237-8, 290, 397,408,457460, (666)

sensitized, 240 Photoisomerization, 198,242-3,245-8, 599, 629, (667) Photolysis, 322-3, 424, 599, (666-7) (see also Flash photolysis) Photomultipliers, 61, 96-7, 222-3 Photoperoxidation, 198-9, 492, 501, 502-4, (667) Photophysical processes, 29-43 (see also Individual processes and parameters) Photoproduct quenching, 170, 173-4, 176,246,633 Photoselection, 221-2, 228, 279, 635, (661) Photostationary kinetics, concentrated solution, 302-4, 378-80 dilute solution, 89, 194-5 DA complexes, 410-12 excimers, 302-4, 320, 378-80 fluorescence, 88-92 fluorescence quenching, 442-3, 512513 phosphorescence, 194-5, 214 photoperoxidation, 502-4 triplet-triplet transfer, 538 Photosynthesis, 599, 627 Photon-sampling fluorometry, 96-7, 109,204,305-6 Phthalic anhydride (PA), 416, 419, 470, 474, (658) Picene (5.9), 13, 73, 133, 182, 184, 228, 252, 260, 276, 281, 455, 460, 463, 477, (650)

Picosecond techniques, 69, 625-6 Piperylene, 198, 598 Platt model (see PFEO model) Polarity, solvent (see Solvent effects) Polyacenes (see Acenes) Polycytosine, 325, 425 Polymers (see also Individual compounds) energy migration, 171,339,518,572, 597-9, 636 energy transfer, 171,572-4,597-9 excimers, 116, 171,325,339, 572,629 fluorescence, 116, 170-1, 325, 597 Polynuc1eotides, 325, 425

Subject Index Polyphenes (see Phenes) Polyphenyls, 108 (see also Individual compounds) Polystyrene, 124,177, 325,339, 572-4, 598-9 Polyvinylbenzophenone, 597-8 Polyvinylcarbazole, 629, 636 Poly-(l-vinylnaphthalene), 325, 598-9 Poly-(N-vinylphthalimide), 598 Polyvinyitoluene, 572 POPOP, 86, 120, 124, 135, 137, (653, 655) Porphyrins, 600 PPD, 124, 134, 136, (653, 656) PPF, 124, 134, 136, (653, 656) PPO, 124, 134, 136, 173, 358, 360, 583, 585,613,(653,656) Pressure quenching, 241-8, 441, 628 Proflavin, 376-8 Proflavin hydrochloride, 374-5 2-Propoxynaphthalene, 322 9-n-Propylanthracene (3.1F), 23, 121, 321, 356, 475, (645) 6-iso-Propyl 1: 2-benzanthracene (4.3U), 24, 358, (649) 5-n-Propyl l : 2-benzanthracene (4.3R), 24,358, (649) iso-Propylbenzene (11), 21, 122, 342, 354, 457, (642) n-Propylbenzene (1J), 21,122,256,342, 457, (642) 9-n-Propyl, 10-bromoanthracene, 121, (646) Propyne bromide, 482, (658) Propyne chloride, 482, (658) Proteins, 600 P-type delayed fluorescence (see Delayed fluorescence, P-type) Pulse fluorometry, 95-6, 102, 109, 305 Pulse radiolysis, 60-1, 581 Pulse shape discrimination, 562 Purification, 91, 530, 534 Pyrazine, 268, 496, (658) . Pyrene (4.1),11,23,239 , 290,466,612, 633, (647) absorption, 62-4, 71, 77-8,81, 118, 268,273,454,459,527,628,631 crystal, 215, 317-19, 323, 325, 328, 330-5,362,425,527,533,556 delayed fluorescence, 36, 63, 215, 373,385-8,392-4,556,632

699

Pyrene-continued electronic states, 71, 78, 184, 259,

290,459,462 excimer, 170, 215, 301-2, 305, 308310, 313-15, 317-19, 323, 325, 328, 330-5, 347, 349-50, 352,

357,360,362,367,369,396,400, 420-2, 425, 428, 436, 450, 475, 478, 510, 556, 627-31 fluorescence, 62, 63, 81, 118, 128- 9, 133, 144, 162, 170-1, 179, 252, 305,308-10,352,357,362,387,

395-6,400,422,425, 430-1,476, 478-9,533, 575,637 phosphorescence, 182, 259, 347,369, 450-1,488, 637 radiationless transitions, 162, 171, 179-80, 182, 185, 187, 201,

230-1,252,287,289,360,395-6, 400,451,479, 630 pyrene·d lO (4.1d), 23, 129, 180, 182, 185,273,280,287,488, (647) 3-Pyrene sulphonate (4.10), 23, 357, 362, (648) 3,5,8,1 O-Pyrene tetrasulphonate (4.1 H), 23,357,362, (648) Pyridine, 268, 453, (658) Pyridoxine, 600 pyromelittic dianhydride (PMDA),

416,470,631 - 2, (658) Quantum counters, 97-8 Quasi-linear spectra, 118-19, 171 p-Quaterphenyl (E), 26, 75, 108, 123, 131,179,277,477, (652) Quenching, collisional, 90-1, 197-8, 246, 434, 441-7,509-11,584-5,589,(667) concentration (see also Excinier formation) singlet state, 91-2, 100, 246-7, 301-4,441, (664) triplet state, 347-8, 369, 447, 450-1, (664) dynamic, 90-1, 434-5, 441-7, 507510,514, (667) energy transfer, 90-1 , 434, 447, 606, (667) (see also Energy transfer) exchange,434-5,442,447- 9,510-13, 635

Subject Index

700

Quenching-continued impurity (see also Quenching by oxygen and nitric oxide) excimer, 338, (665) singlet state, 36, 40, 90-1, 173-4, 197- 8, 209-11, 395, 433-47, 481-2,484-5, 584-5,589,597, 613, (664) triplet state, 42, 447-51 , 486-7, 606, (664)

ionization, 342, 562 oxygen, singlet state, 35, 90-1, 110, 173, 442, 444, 492, 496-504, 506510, 514-15, 584, 613, 635, (664) triplet state, 206, 344, 442, 447-9, 492,500-4,599, (664) nitric oxide, singlet state, 110, 442, 493, 504-8, (664) triplet state, 442, 447- 9, 493, 504-8, (664) paramagnetic ions, 447-9, 486- 7, 495 photochemical, 439-41, 485 photoproduct, 170, 173-4, 176, 246, 633 pressure, 241-8, 441, 628 static, 434-5, 441-7, 506-8,538 surface, 531, 533,536-7,565-6, 611 transient dynamic, 444-7, 509 weak,444 Quinine sulphate, 97-8, 200, (685) Quinoline, 235, 268, 605, (658) Quintet state, excimer, 40, 366, 394 exciplex, 41 ground state, 236-7 Radiationless transitions, 142-92 (see also Internal conversion, Intersystem crossing) Radiative transitions (see Absorption , Fluorescence, Phosphorescence) adiolysis, pulse, 60-1, 581 aman scattering, 63, 625 Rate parameters, 36-42, 305-8 (see also Individual processes and parameters) Reaction kinetics (see Photostationary kinetics, Transient kinetics)

Recombination, fluorescence, 373, 398-9, (662) phosphorescence, 373, 398-9, (663) Reduction potential, 427-8, 434, 482 Refractive index, influence on (see also Solvent effects) absorption spectrum, 86, 110-16, 138, (660)

excimer radiative lifetime, 310, 312 fluorescence quantum yield, 98-9 fluorescence spectrum, 86, 98, 110116, 138, (661) molecular radiative lifetime, 87-8, 103,312,626 oscillator strength, 51-2, 110,138 Rhodamine B, 98, 120, 207, 254, 591, " 617-18, (658) Rhodamine 6G, 207, 254, (658) Riboflavin, 600 Ribonuclease, 433 RNA, 600 Rubrene (R), 26, 120, 131, 179, 277, 341,628, (653) Ruby laser, 60-4, 67-8, 76, 79, 166,560, 563 Sandwich, dimer, 322-3, 339, (665) mixed dimer, 323, 424 Saturated hydrocarbon fluorescence, 636,638 Scintillator solutes, 102, 108-9, 124, 134-7, 434,576, 613 Scintillation, crystals, 529, 532-3, 562 delayed (see Scintillation slow component) fluid solutions, 576, 580-90, 613 plastic solutions, 572-4 process, 29, 562,580-90 pulse shapes, 574 response anisotropy, 532-3 slow component, 533, 562, 566, 582, 611 solutes (see Scintillator solutes) Selection rules, 8-10, 65-8,151,161-2, 216,222,224,563,625, (660)

Self absorption, 92-3, 98-100, 103,425, 521-2,536-7,(667) Sevron yellow GL, 575, 612, (659)

Subject Index Sevron yellow L, 575,612, (659) Shpol'skii effect, 118-19, 171 Siebrand model (radiationless transitions), 152-62, 167,200 Singlet manifold, 29-30 'Single-photon' technique (see Photonsampling fluorometry) Smoluchowski relation (diffusion), 312-13,445-6 Sodium fluorescein, 617, (659) Sodium iodide, 437, 484 Solvated excited molecules, 164-6, 626 Solvent effects (see also Refractive Index, influence of) absorption spectrum, 107, 109-19,

701 trans-Stilbene (M), 27, 268, 453, 460, 4fi1, 406, 533, (653) Stokes' l~w, 313, 511 Stokes-Einstein relation (diffusion), 312-13,443, 509-13 Stokes shift (spectra), 108-9 Styrene, 212, 268, (659) Sulphonamides, 600 Sulphur dioxide, 444 Sulphur hexafluoride, 217 Sunlight, effect of, 600 Surface quenching (see Quenching, surface) Symmetry, 9-10,151,161, 224,569

138,165, 188,527-8,626, (660) exciplexes, 428-32, 478- 9, 633, (662) fluorescence spectrum, 107, 109-19, 138,164-6,188,626,(661) Sp - SI internal conversion, 175, 189, (663) T 1 - So intersystem crossing, 267, 294- 6, 633 Solvent-shared ion pair, 429-30, 438-9, 513 Specific solvent interactions, 113, 116119,250 Spectrometry, delayed fluorescence, 201-6 excitation, 214-17 phosphorescence, 201-6 So - To absorption, 211-18 threshold electron impact, 216-18 T 1 - To absorption, 218-22 (see also Flash photolysis) Spin-orbit interaction, 8, 68, 161, 167, 208-11, 226-8, 230-4, 236, 285,

343,418, 495,(660) Spirans,597 Static quenching (see Quenching, static) Stern-Volmer, coefficient, concentration quenching, 301-4, 320,441 impurity quenching, 434, 441-7, 449, 481-2, 487, 508-9, (664-5) kinetics, 36-7, 570-4 relation, 441-3 cis-Stilbene, 268, (659)

m-Terphenyl (J), 26, 182, 261, 277, 464, (653) o-Terphenyl(L),27, 262, 277,460,464, (653) p-Terphenyl (D), 26, 46, 75, 104, 123, 130, 134, 136, 179, 182, 230-2,

253-4,261,277, 287, 289,460,477, 488,522-3,533,537,576, 581,585, 588,613,632,637,(652) p-Terphenyl'd 14 (Dd), 123, (652) 1: 2: 3 :4:5: 6: 7: 8-Tetrabenzanthracene (7.5), 17, 182, 260, (651) I : 2 : 3 : 4 : 5 : 6 : 10 : 11-Tetrabenzanthanthrene (10.2), 19, 182, 261, (651) 5 : 6 : 8 : 9: 14: 15 : 17: 18-Tetrabenzoheptacene (11.1), 19, 182, 261, (651) 1 : 2: 3 : 4 : 5 : 6: 7: 8- Tetrabenzonaphthalene (6.16), 16, 260, 263, (651) 1: 2: 3: 4: 6: 7: 12: 13-Tetrabenzopentacene (9.3), 18, 182, 260, (651) 1,2,4,5-Tetrabromobenzene, 257, (643) Tetrabromophthalic anhydride (TBPA), 418-19, 470-3, (659) Tetracene (4.2),3 , 11,23,239,290, (648) absorption, 56, 71, 81,118,238, 273,

280,454,459,527 crystal, 238, 362, 459, 527, 529, 531,

. 533-4,536-7,557,563-4,603 delayed fluorescence, 542, 557 electronic states, 71, 179, 184, 459, 463 excimer (dimer), 317,362,367

702

Subject Index

Tetracene-continued fluorescence, 81, 107, 111-12, 118, 123,129,133,179,252,341,362, 440, 476, 502-4, 531, 533-4,

536-7,563,603 phosphorescence, 182, 506 photoperoxidation, 502-4 radiation less transitions, 111-12, 179,182,185,199,201,252 Tetracene·d 12 (4.2d), 24, 185, (648) 1,4,5,8-Tetrachloroanthracene, 258, (646) 1,2,4,5-Tetrachlorobenzene (l N), 21, 256, (643) Tetrachlorophthalic anhydride (TCPA), 415-19, 468-73, 631-2, (659) 1,2,4,5-Tetracyanobenzene (TCNB),

416-17,419,470,474,(659) Tetracyanoethylene (TCNE), 452-3, 456, (659) Tetraiodophthalic anhydride (TIPA),

419,470, (659) 1,2,3,5-Tetramethylbenzene, 344, 368, (641) 1,2,4,5-Tetramethylbenzene (see Durene) N,N'-Tetramethylp-phenylenediamine, 399 Tetranitromethane, 482, (659) Tetraphene(see] : 2-Benzanthracene)'Tetraphenyls, 265, (659) 1,1 ',4,4'-Tetraphenylbutadiene (TPB),

120,124,522-3,573-4,576,(659) Thermoluminescence, 398- 9 Thionaphthene, 268, 530, 535, 557-9, (659) Threshold electron impact spectrometry, 216-18,224 Thymine, 325, 600 Toluene (lA), 20, 465, (641) absorption, 62, 70, 77-8, 268-9, 454 electronic states, 62, 70, 78,408, 457, 462 energy migration, 580-90, 614- 15 energy transfer, 583-90, 613 excimer, 62, 176, 310, 342, 351, 354,

360,581,615,629 fluorescence, 122, 126, 178, 247, 292, 310,342, 351,354,434,440,482, 589-90,616

Toluene-continued liquid, 62, 171, 189, 310, 342, 354, 434,482,580- 90,613-16,629 phosphorescence, 256, 417, 470, 628 radiationless transitions, 174-6, 178,

180,189-90,234,247,286,293, 360,628 vapour, 247, 292-3 Toluene·d B (lAd), 20, 122, 126, 178, (641) Toluidine, 398 9-n-Tolylanthracene, 121, (645) Total ring quantum number, 6 Transient dynamic quenching, 444-7, 509 Transient kinetics, concentrated solution, 304- 9, 380- 4 dilute solution, 89, 195 excimer, 304-9, 380-4 molecular fluorescence, 88- 92 phosphorescence, 195 singlet-singlet transfer, 570-1 triplet-triplet interaction, 380-4, 389- 90,560 triplet-triplet transfer, 541 vapour, 244 Transition moments, charge-transfer, 409-10 electric dipole, 50-1, 65-8,149,224-8 electric quadrupole, 65- 7 electronic, 50-1 multiphotonic, 65--8 magnetic dipole, 65- 7 vibronic,50-1 1: 2: 3:4: 5: 6-Tribenzanthracene (6.9), 15, 133, (650) 1 : 12 : 2 : 3 : 10 : 11 - Tribenzoperylene (8.5), 18, 182, 260, (651) 1,3,5-Tribromobenzene, 257, 343, 368, (643) 1,3,5-Tri-t-butylbenzene, 465, (642) 1,5,1O-Trichloroanthracene, 258, (646) 1,3,5-Trichlorobenzene OM), 21, 256, 343, 368, (643) Triethylamine, 408, 427, 437, 476, 481, 632, (659) 1,3,5-Triethylbenzene, 465, (641) 1-Trifluoroacetylazulene, 166 Trifluorobenzene, 268, (642) 1-4-bis-(Trifluoromethyl)-benzene,122, (642)

Subject Index Trimethylamine, 481, (659) 1,2,3-Trimethylbenzene, 457, (641) 1,2,4-Trimethylbenzene (lG), 21, 122, 126,178,457, (641) 1,3,5-Trimethylbenzene (see Mesitylene) 2,4,6-Trimethylbenzonitrile, 433 2,3,5-Trimethylnaphthalene (2M), 22, 355,454,458, (644) 1,3,5-Trinitrobenzene (TNB), 404, 408, 409, 415, 419, 437, 452- 6, 465-6,

468-70, (659) Triphenylalkanes, 324, 364- 5, (659) Triphenylamine, 124, 605, 617, (659) 1,3,5-Triphenylbenzene (K), 27, 124, 131,182,262, (653) Triphenylene (4.6), 12, 25, 466, 606, (649) absorption, 62, 72, 77-8, 81 ,222,275, 281,455,459 crystal, 362 electronic states, 62, 72, 78, 179, 184, 459,463 excimer, 330, 362, 367 fluorescence, 81, 123, 129, 133, 179, 186,231,252,254,362,476 phosphorescence, 182, 186, 254, 260,

417,470,488 radiationless transitions, 179, 182, 185,187,201,231 , 235,252,254, 287,289 Triphenylene·d 12 (4.6d), 25, 123, 129, 179,182,185-6,252,254,287,289, 451,488, (649) Triple exciplex, 633 Triplet state, 193-300 absorption (see Absorption, So - T\ and T\ - Tq) energy migration (see Energy migration, triplet) energy transfer (see Energy transfer, triplet) excimer (see Excimer triplet state) exciton (see Exciton, triplet) ground state, 236, 492 intersystem crossing (see Intersystem crossing) lifetime, 148-9, 152, 168, 177, 182, 195, 207-8, 211, 248- 50, 264- 7, 369, 372, 374, 382-5, 418-19, 448-51, 472-4, 488, 545, 547,

703 Triplet state-continued 565-6, 599, 627-31, 633, 637, (663) lifetime determination, 205, 388 manifold, 29-30 oxygen quenching, 206, 344, 442, 447- 9,492,500-4,599 phosphorescence (see Phosphorescence) quantum yield, definition, 194, 377, 378-9 determination, 195-200, 242-3, 394-7, 543-4 values, 200- 1, 229, 243, 251-4,

293,400,627,637, (664) sensitized fluorescence, 200, 206-7, 519-20,523,590-1,617-18 sensitized isomerization, 198, 200, 242-3,245-8,599,629 Triplet-triplet absorption (see Absorption, To - Tq and T\ - Tq) Triplet-triplet interaction association processes, 36, 40, 62-3, 239,340,373,389-94,433,447, 520- 1, 533, 599, (665) energy migration (see Energy migration, triplet-triplet) energy transfer (see Energy transfer, triplet-triplet) exciton (see Exciton, triplet) fluid solutions, 239, 340,373,378-89, 391-4, 513, 520-1, 631- 2, (655) heteropolar, 433, 521, 542- 3, 549-55 liquids, 582, 632, (665) magnetic field effects, 563-4 mixed crystals, 548-59 polymers, 340,598-9, (665) pure crystals, 63, 215-1 6, 340, 373,

533,559-67,610-11, (665,667) rigid solutions, 373, 389- 90, 520-1, 590-2, (665) vapours, 632 'Trivial' process, 522 (see Energy transfer, radiative) TrypafIavin, 376,617, (659) Tryptophan, 433, 600,617, 626, (659) Tyrosine, 600 Unimolecular processes, 30-32, 36-8 (see also Individual processes and parameters)

704 Universal solvent interaction, 113- 16 Uracil, 424-5, 600 'Variation of energy denominators', 547 Vavilov's law, 142-4, 161-2, 164,172, 177,234-5, 377-8 Vibrational, distortion, 177, 248, 451 energy transfer, 110-12 modes,45-6,52-4, 85-7, 106, 152-8, 218,248- 50,628 relaxation, 69, 110-12, 142, 150-1 , 235, 247,626 structure, 45-6, 112, 116-19, 157, 208,218, 241,249-50,291 overlap integral, 51, 149- 50 (see also Franck-Condon factor) Vibronic, states, 44-6, 50, 67, 106-8, 110-12, 142,240-1 transitions, 44-6, 50-2, 84-7, 142, 149- 52, 244, 291, 525, 527-8, 602 9-Vinylanthracene, 123, (645) 4-Vinylbiphenyl, 123, (652) Violanthrene, 238, 460, 603, (659) Vitamins, 600 Voltz model (energy migration and transfer), 578-80, 583-90 Weak quenching, 444 Wurster's Blue perchlorate, 433

Subject Index Xanthone, 605, (659) Xenon, 198,210,436 X-traps, 535, 557-9 m-Xylene (lC), 20, 70, 122, 126, 178, 256,292-3,342,354,408,454,457, 465, (641) a-Xylene (lB), 20, 70, 122, 126, 178, 256,292-3,342, 354,454,465, 630, (641) p-Xylene (lD), 20, 465,629, (641) absorption, 70, 269, 454 electronic states, 70, 457 energy migration and transfer, 580590, 613-15 excimer, 176, 342,344- 5,351,354, 615 fluorescence, 122, 126, 178, 292, 342, 344- 5,351,354,440,616 liquid, 171, 189, 342, 344- 5, 354, 580-90,613- 16 phosphorescence, 256 radiationless transitions, 174-6, 178, 180,189-90,286, 293 vapour, 292-3 p-Xylene -d 1o (lDd), 20, 122, 126, 178, (641) Y okota- Tanimoto theory transfer), 577-80

(energy

Zeeman levels, 8 Zero-point vibrations, 46, 107, 332-4, 545